,M5:r.NRLF 


^B   53S 


M 


c'C'-^ 


A 

COMPLETE  KEY 

TO 

NEW  FEDERAL  CALCULATOR, 

OE 

IN  WHICH  THE 

METHOD  OF  SOLVING  ALL   THE  QUESTIONS  CONTAINED 
IN  THAT  WORK  IS  EXHIBITED  AT  LARGE. 

designed 

to  facilitate  the  labour  of  teachers,  and  assist 

those  who  have  not  the  advantage  of  a 

tutor's  aid. 


BY  THOMAS  T.  SMILEY, 

TEACHER. 

Author  of  an  Easy  Introdaction  to  the  Study  of  Geography.    Also, 
of  Sacred  Geography,  for  the  use  of  Schools. 


PiaatrrtjjJxta: 


PUBLISHED  AND  FOR  SALE  BY  J.  GRIGG,  No.  9,  NORTH  4th  St. 

AND  FOit  SALE  BY  BOOKSELLERS  AND  COUNTRY 

MERCHANTS  GENERALLY  IN  THE  SOUTHERN 

AND  WESTERN  STATES. 


joMpi  ^'Vnci-i- 


Qcil  &  Mechanical  Engineer. 

aAtf  FRANCISCO,  GAL. 


GiFT 


Eastern  District  of  Pennsylvania,  to  wU: 
*********      BE  IT  REMEMBERED,  That  on  the  ninth 
I  T    g  *  day  of  May,  in  the  forty-ninth  year  of  the  Tnde- 
I      *     *  t  pendence  of  the  United  States  of  America,  A.  D. 
*********  1825,  John  Grigg,  of  the  said  district,  hath  de- 

Eosited  in  this  office,  the  title  of  a  book,  the  right  whereof 
e  claims  as  proprietor,  in  the  words  following,  to  wit : 

"  A  Complete  Key  to  Smiley's  New  Federal  Calculator, 
or  Scholar's  Assistant;  in  which  the  Method  of  ►Solving  all 
the  Questions  contained  in  that  Work  is  exhibited  at  large. 
Designed  to  facilitate  the  labour  of  Teachers,  and  a?^sist 
those  who  have  not  the  advantage  of  a  Tutor's  aid.  By 
Thomas  T.  Smiley,  Teacher.  Author  of  An  Easy  Intro- 
duction to  the  Study  of  Geography.  Also,  of  Sacred  Geog- 
raphy, for  the  use  of  Schools." 

In  conformity  to  the  act  of  the  Congress  of  the  Unitrd 
States,  entitled,  "  An  Act  for  the  encournj^tMncnt  of  learn- 
ing, by  securing  the  copies  of  maps,  charts,  and  books,  to 
the  authors  and  proprietors  of  sucii  copies,  during  the  times 
therein  mentioned."  And  also  to  the  Act,  entitled,  "An 
Act  supplementary  to  an  Act,  entitled,  '  An  Act  for  tiie 
encouragement  of  learning,  by  securing  the  copies  of  maps, 
cuarts,  and  books,  to  the  authors  and  proprietors  of  such 
copies,  during  tlie  times  tlierein  mentioned,'  and  extending 
the  benefits  thereof  to  the  arts  of  designing,  engraving,  and 
etchings  historical  and  other  prints." 

D.  CALDWELL,  C/erA:V  ^/le 

Eastern  District  of  Pennsyhania. 


Stereotyped  by  J.  ilowc. 


3L> 


nSo 

CONTENTS. 

Paffc 

Simple  Addition, 

- 

Multiplication, 

. 

7 

Subtraction, 

. 

10 

Division, 

. 

11 

Long  Division,    - 

- 

13 

Compound  Addition, 

- 

20 

Compound  Multiplication, 

. 

26 

Compound  Subtraction, 

- 

33 

Compound  Division, 

- 

43 

Reduction, 

. 

43 

Single  Rule  of  Three,    - 

. 

61 

Double  Rule  of  Three,  - 

, 

69 

Practice, 

- 

73 

Tare  and  Tret,  - 

. 

87 

Interest,              -    . 

. 

94 

Compound  Interest, 

- 

100 

Insurance,  Commission  and 

Brokage, 

104 

Discount, 

- 

lOG 

Equation, 

- 

109 

Barter,    - 

- 

110 

Loss  and  Gain,   - 

. 

112 

Fellowship, 

. 

IIG 

Kxchange, 

- 

119 

Vulgar  Fractions, 

. 

121 

Decimal  Fractions, 

. 

127 

Position, 

■- 

132 

Involution,  or  the  Raising  of  Powers, 

141 

E/olution,  or  the  Extracting 

of  Roots 

1 " 

t7>. 

Alligation, 

. 

147 

Arithmetical  Progression, 

. 

149 

Geometrical  Progression, 

- 

151 

Compound  Interest  by  Decimals, 

1.52 

Annuities  at  Compound  Interest, 

ir;.3 

Annuities  in  Reversion, 

. 

154 

Perpetuities  at  Compound  Interest, 

ih. 

Combination, 

. 

ih. 

Permutation, 

. 

155 

Duodecimals, 

- 

ib. 

Promiscuous  Examples, 

" 

* 

158 

iviS03795 


EXPLANATION  OF  CHARACTERS. 

Signs.  Significations. 

=  •   Equal;  as  20s. =£1. 

-f  Addition,  (or  more)  as  6-f  2=8. 

—  Subtraction,  (or  less)  as  8 — 2=6. 

X  Multiplication,  (or  multiplied  by)  as  6  X  2=12. 

-^  Division,  (or  divided  by)  as  6-f-2=3. 

:  : :  :       Proportionally ;  as  2  :  4  :  :  6  :  12. 
^J  or  "^-J     Square  Root:  as  ^^64=8. 
y  Cube  Root;  as  ^64=4. 

A  vinculum ;  denoting  the  several  quantities 

over  which  it  is  drawn,  to  be  considered 
jointly  as  a  simple  quantity. 


JOHN  S.  PI^ELL. 

QoS  &  Mechtudcal  Engineer, 


HAJA  JfkiLf^CiaCO, 

A  KEY 

CATi, 

Etit  S-ettt  iFeTretal  ealculatot^ 

~mt9®9*^ 

SIMPLE  ADDITION. 

EXAMPLES. 

(8)       4829 
1234 
6101 
3014 
5618 

(9)       91769 
14678 
80032 
71897 
76989 

(10) 
(13) 

(16) 

876994 
213678 
482906 
809769 
376980 

20796 

335365 

2760327 

(11)     389261 
789794 
849798 
487697 
999996 
948219 

(12)    2136784 
8297698 
8297694 
4897695 
1234697 
7092032 

3769694 
4976082 
4569761 
8213243 
4876962 
4876920 

4464765 

31956600 

31282662 

(14)     37856 

975 

1234 

14 

5612 

2075 

16287 

(15)     378269 

402607 

702 

1246 

2132 

45178 

10276 

141 

5672 

82971 

34676 

1459 

427 

12 

64053 

840410 

125358 

A  2 

6 

SIMPLE  ADDITION. 

(17)  14 
16 

23 
29 
80 
31 
100 

293 

(21)  365 

807 

660 

25 

37 

101 

1895 

(24)  35    ( 
21 

66 

(18)  36 

97 

125 

384 

1176 

1818 

(19) 

3797 

9^ 

2 

75 

876 

9750 

(20)  205 

20 

340 

970 

367 

1001 

3403 

14595 

(22)    300 

75 

2 

47 

33 

9784 

20150 

765091 

1075047 

(23) 

tSES. 

(27)  60 

25 

125 

216 

416 

75960800 

225000 

140 

76185940 

Miles, 

(28)  37 

33 

40 

35 

145 

1870529 

PRACTICAL  EXEBC 

25)  275    (26)  30 
196       12 

5 

471       — 

g47 

Sheep, 

(29)  A's  34 

B's  47 

C's  64 

135 

(30)  25 

15 

40 

9 

89 

(31)  8 
15 
19 
12 

64 

bar.          $ 
(32)  400  for  2000 
550    2750 

950 

$4750 

L 

"*"" 

"~" 

MULTIPLICATION.  7 

MULTIPLICATION. 

CASE  L 

EXAMPLES* 

(8)  3948769768     (9)  87051298    (10)  976201698769 
3  4  5 


11846309304 


348205192 


488100849384{^ 


(11)  456978426976  (12)  8079698769  (13)  97698429769 
6  7  8 


2741870561856 


(14)   28769842369 
9 

258928581321 


(16)   5697698976845 
11 

'62674688745295 


(18)   84976876989 
12 


56560891388 


781587438152 


(15)   769829769478 
10 

7698297694780 


(17)   7029876956 
12 


1019722523868 


(20)  4218    (21)  7S21 


84358523472 


(19)   9021681409671 
12 

108260176916052 


(22)  87692    (23)  95698 
4  5 


8436 


21963 


350768 


478490 


(24)  10691   (25)  31078   (26)  109019    (27)  900078 
6  7  8  9 


64146 


217546 


872152 


8100702 


8 

(28)  826870 
10 

MULTIPLICATION. 

(29)  278976 
11 

(30)  12569769 
12 

8268700 

(34)  39786948 
197 

3068736 

150837228 

CASE  2. 

EXAMPLES. 

(35)  4978829 
408 

(36)  8735698 
570C 

278508636 
358082532 
39786948 

39830632 
19915316 

52414188 
61149886 
43678490 

2031362232 

7838028756 

49845892788 

(38)  49569876 
4817 

(37)  84016978 
3761 

(39)  9637842 
9078 

84016978 
504101868 
588118846 
252050934 

346989132 
49569876 
396559008 
198279504 

77102736 
67464894 
86740578 

87492329676 

315987854258 

238778092692 

(42)  11271 
35 

(40)  9786 
13 

29358 
9786 

(41)  8475 
29 

•  76275 
16950 

56355 
33813 

127218 

245775 

394485 

'1 

(43)  19004 
305 

MULTIPLICATION. 

(44)  76976 
489 

9 

(45)  84769 
976 

95020 
57012 

692784 
615808 
307904 

608614 
693383 
762921 

5796220 

37641264 

82734544 

(46)    1978987 
4809 

(47) 
49 

9807094 
6047 

17810883 
15831896 
7915948 

68649658 
39228376 
035470 

9516948483 

49496403418      1 

(48)  37|00 
2|00 

CASE  3. 

EXAMPLES. 

(49)  4870 

25|00 

(50)  4087  00 
906  000 

740000 

24350 
9740 

24522 
36783 

12175000 

370282200000 

(51)    876956 

99 10000 

7892604 
7892604 

868186440000 

10 

SUBTRACTlOJs. 

CASE  4. 

exampj.es. 

(53)  8976 
6 

(54)  769G           (55)  87698 
9  V                         9 

(56)  20784 
12 

5,3856 

69264                  789282 

249408 1 

8 

9                            8 

9] 

430848 

62337G   ■■■  '^'     6314256 

2244072 

(57)  81207 
11 

(58)  ^7696         (59)  75687 

12               -          7 

1 „ ,   ; .              .   

(60)  34075 
6 

893277 

572352               529809 

204450; 

12 

12                          8 

e' 

10719324 

6868224             4238472 

1226700' 

PRACTICAL  EXERCISES. 

(61)  ^25 
5 

(62)15              (63)  g250 
4                             7 

(64)  gl50i 

4\ 

§125 

(65)  glOO 
25 

60                      ^1750 

{66)  18175 
14 

Or  thus,     100 
5 

500 

500 

72700 

200 

5 
g2500 

18175 

^2500 

254450' 

.i*»9®d«^ 

SUBTRACTION. 

EXAMPLES. 

(1)    859708 
124978 

(5)    0076048                (6) 

5321478781 

7940689 

139876956 

734790 

1135359 

392270922 

-, ; ^ T-^l 

DIVISION.                   1 1 

(7)  100000 
84321 

(8)  75381478       (9)  102070845 
39040217           19768799 

15671? 

36341261           82302046 

(10)  196   ( 
37 

159 

11)  487   (12)  875   (13)  967    (14)  1001 
96      302      351        487 

391      573      616        514 

(15)  9765 
1307 

8458 

(16)  87696    (17)  455692  "*  (18)  1000000 
10091       300120           1 

77605       155572       999999 

PRACTICAL  EXERCISES. 

(19)  25  (20) 
8 

75  (21)7896  (22)4875  (23)1240  375 
42      4389      2976      1082  567 
...         .—        ....       .,_     1  ,^10 

17 

33     3507     1899     ^158  

_     Sum  1082 

(24)  5487 
2075 

3412 

325          (25)  25  containing  250 
750               9          75 

1000 

16         175 

2075  Sum. 

.MH«Q9««»- 

DIVISION. 

EXAMPLES  OF  SHORT  DIVISION. 

,(7)  2)56789^ 
28394^ 

mn     (8)  3)3729768769   (9)  4)469769876 

^4       1243256256+1     117442469 

,   ,  -   ,   , ^1 

12 

DIVISION. 

(10) 

6)849768769                        (11)      6)756976874 

169953753+4                                   126162812+2 

(12) 

7)87694213628                       (13)      8)80269687 

(14) 

12527744804                                        10033710+7 

9)376948769                       (15)       11)876956788 

(16) 

41883196+5                                      79723344+4 

12)4976876946782           (17)  12)89769762048769 

(18) 
(21) 

414739745565+2                      7480813504064+1 

2)3976               (19)     3)8769                 (20)     4)47876 
1088                              2923                                 11969 

5)8767             (22)     6)9698             (23)     7)97899 

(24) 

1753+2                      1616  +  2                      13985+4 

8)80409         (25)     9)981021       (26)     10)897697 

10051+1                  109002+3                    89769+7 

(27)     11)9876978                         28)     12)4967844 

897907+1                                     413987 

PRACTICAL  EXERCISES. 

(29)  2)12         (30)  7)350         (31)  8)8736           (32)  3)3966 
6                        50                  4)1092                       1322 

273 

■    .      ■ 

LONG  DIVISION. 

LONG  DIVISION. 

EXAMPLES. 


13 


(35)     13)875(67 
78 

95 
91 


(38)  28)1475(52 
140 

75 
56 

19 


(41)   41)256976(6267 
246 

109 
82 

277 
246 

316 
287 

29 


(36)  15)476(31 
45 


26 
15 

IT 


(37)  18)958(53 
90 

58 
54 


(39)  31)4277(137  (40)  37)25757(695 
31  222 


117 
93 

247 
217 

30 


335 
333 

227 

222 


(42)  48)337979(7041 
336 

197 
192 

59 
48 

11 


14 

LONG 

DIVISION. 

(43)  59)997816(16912 
59 

(44)  98)999987695(10203956 
98 

407 

199 

354 

196 

538 

387 

531 

294 

71 

936 

59 

882 

126 

549 

118 

490 

8 

595 

588 

7 

(45)1 

^25)4697680424(3758144: 
375 

947 

J   (46)  396)387690204886(979015668 
3564 

3129 

875 

2772 

726 

3570 

625 
1018 

3564 

620 

1000 

396 

180 

2244 

125 

1980 

554 

2648 

600 

2376 

542 

2728 

500 
424 

2376 

3526 

375 
49 

3168 

358 

LONG  DIVISION.  1 5 

C47)    876)4876020048769(5560232932         (48)    1478)8769820000402(5933576454 
4380  7390 


4960  13798 

4380  13302 


^37 


5802  4962 

5256  *  4434 

5460  5286 

5256  4434 

2040  8520 

1752  7390 


2884  11300 

2628    •  10346 


2568  9540 

1752  8868 


8167  6724 

7884  5912 


2836  8120 

2628  7390 

2089  7302 

1752  5912 


1390 


16                 LO^ 

(49)  S7G96)987G97G8720497(112G2 
87696 

\G  DIVISION. 

74501  (50)97680 

89768214100( 
30940 

00O0)8976478976|000OC91896 
87912 

110737 
87696 

18527 
9768 

230416 
175392 

87598 
78144 

550248 
526176 

94549 
87912 

240727 
175392 

66377 
58608 

77696 

653352 
613872 

)00(3242  Ans. 

394800 
350784 

440164 
438480 

168497 
87696 

80801 

(51)  1476980|00000)47 
44 

3588282 
2953960 

Rem 

6343221 
5907920 

4353014 
2953960 

.  1399054 

LONG  DIVISION 

.' 

PRACTICAL  EXERCISES.                                            1 

(52) 

45)9847(218 
90 

84 

45 

(53) 

391)1259678(3221 
1173 

866 
782 

397 
360 

847 
782 

Rem.  37 

658 
391 

Rem.  267 

(54) 

148)225476(1523 
148 

(55) 

25)375(15  bushels. 
25 

774 
740 

125 
125 

347 
296 

516 

444 

Rem.  72 

L= 

B  2 


18                                        LONG  DIVISION.                                               || 

(56)      75)87735840(1169811 
75 

127 
75 

(57)     49850)99700(2 
99700 

523 
450 

735 
675 

608 

600                  * 

• 

84 
75 

90 
75 

15  Rem. 

When  the  divisor  is  the  exact  product  of  any  two 
;  figures  multiplied  together. 

EXAMPLES 

(61)     5)9756                          (62)     i 
7)l951-fl  1st  Rem. 

))8491 
9)943+4 

278+5  2d  Rem. 
X5 

25+1=26 

104+7x9+4=67 

(63)     9)44767                           (64) 

7)92017 

2)4974+1  Rem. 

2487 

1643+1x7+2=9 

1 

LO:SG  DIVISION.  19 

(65)     11)55210  {6G)     6)38751 


9)5019+1  8)6458+3 

Rem.  — Rem. 

557+6X11+1=67  807+2x6+3=15 


(67)     12)99876                 (68)  12)379^7 

9)8323  12)3163+11 

— —  Rem.  :  Rem. 

924+7x12=84  263+7x12+11=95 


PRACTICAL  EXERCISES. 

(69)     5)3775  (70)     12)480  (71)     12)14400 


5)755 
Ans.  151 

8)40 
Ans.  5  fe 

12)1200 
Ans.  100 

(72)   12)1800 
6)150 

(73)   12)396 
11)33 

Ans.  25 

Ans.  ^3 

EXAMPLES  IN  ADDITION,  MULTIPLICATION,  SUBTRACTION 

AND  DIVISION. 
(I)     50  (2)     40     10  (3)     25000 

50  20     10  13000 


100  2)20     20  2)12000 

—25 


Ans.  10                                        g6000 
75  Ans.  —  


20 

COMPOUND   ADDITION.                                         1 

(4)  Bought  8200  Sold  3756       (5)  50)2450(49  mUes.  Ans. 
5000           4879                   200 

13200            8635                     450 

8635           450 

Ans.  4565                                                                    1 

(«) 

Bought  24  bags,  containmg  3000  fe 
Sold       15                                 1736 

Remains  9  bags,  containing  1264  ^ 

(7)  Days  '365)2920(8  dols.  per  day.     Yearly  income  2920 
2920                               Spends  yearly  1769 

Savesper  year  $1151 

i.. 

-^©a*.^ 

COMPOUND  ADDITION. 

l^'EDERAL  MONEY. 

EXAMPLES. 

$ 

ct8,  m,                     $     cts.                        g     cis. 

(2)     46 
79 

75     5              (3)     37     68J              (4)     72     62- 
37     8                       95     371                        85     87l 

43 

50     0                       43     25"                        20     12| 

97 

37     5                        79 .  56}                        45     ISJ 

91     37' 

g267 

00     8                   g255     87i                       42     68| 

g440     06» 

COMPOUND  ADDITION 

21 

$     cts. 

g 

cts. 

i 

'  cU. 

(5)   54  75 

(6)  29 

25 

(7)   1 

182 

3^  371 

34 

371 

2 

50 

93  18|. 

188 

68| 

871 

149  871 

603  68| 

979  121 

2194  181 

265 
1783 

121 

18| 

1 

93J 
87o 
68| 

8579 

56| 

2 

6 

87i 

372 
87- 
93i 

g4012  18J 

P 

0887 

06J 

^ 

1 

$ 

els. 

$13 

25 

Ct8, 

(8)    5 

00 

(9) 

1 

871 
681 

18 

60 

1 

8 

87^ 

0 

433 

1 

18| 

1 

371 

14 

50 

0 

933 

0 

871 

0 

56J 

5 

371 

87| 

0 

37f 
3l| 

7 

0 

20 

00 

STERLING  MONEY. 

0 

121 

^82 

18| 

$l_ 

683 

EXAMPLES. 

£  s. 

d. 

£ 

*.  d. 

£ 

*.  rf. 

(2)   7  9 

6| 

(3) 

4 

6  4 

(4)  565 

3  7 

13.  7 

47 

19  7 

382 

13  5 

4  5 

2 

159, 

5  3 

592 

9  2 

10  18 

lOj 

78 

6  llj 

856 
259 

17  3 
9  8 

Ans.  36  1 

0 

Ans. 

289  18  IJ 

An 

3.  2656  1 

3  1 

22             <^03irOl  ND  ADBITIOX. 

_— 

£      S.     d. 

£  s. 

d. 

£  s. 

d. 

(5)  142  16  7    (6) 

763  7 

4 

(7)  69   18 

7 

489  3  4 

39  4 

9 

175  2 

6 

726  15  9 

162  17 

2 

1582  19 

4 

573  4  '8 

459  15 

0 

175  13 

9 

628  12  6 

473  12 

8 

143  13 
212  0 

8 
7 

Ans.2560  12  10   Ans.  18^8  16 

11 

Ans. 
£ 

2359  8 

5 

£  s.     d. 

s.    d. 

(8)   1776  12  8 

(9) 

985 

4  9 

412  16  5 

186 

13  4 

369  7  2 

1569 

18  4 

469  15  10 

183 

0  8 

573  19  2 

^ 

0 

17  4 

1987  14  8 

0 

0  7 

4823  15  11 

Ans. 
EIGHT 

2925 

15  0 

Ans.  10414  1  10 

POIS  WJ 

AVOIRDU 

T.  cwt.  qr.  lb.  oz,  dr. 

T.  cwt.  qr.  lbs.  oz. 

dr. 

(2)   7  11  2  16  4  13 

(3)  12 

16 

1  19  15 

0 

15  7  3  8  16  7 

114 

io 

2  12  4 

13 

138  19  1  12  8  13 

72 

4 

2  24  14 

3 

42  8  3  19  12  4 

176 

15  . 

3  4  15 

11 

357  6  2  8  3  3 

Anp  '^'^ft 

7 

2  6   1 

11 

Ans.  561  14  1  7  13  8 

qr.  lb.  0 

z.dr. 

T.  cwt. 

(4)   139  19 

3  18  1 

13  10 

1754  10 

2  11 

2  14 

27  ,  3 

0  14  11  0 

0  13 

0  0  13  0 

Ans.  1922  6 

.2  17 

8  8 

^^i;^^,;^;^^ 

COMPOUND  ADDITION.                                 23 

TROY  WEIGHT. 

lbs.    oz.dwts.gr.           lbs.  oz.dwts.gr.           lbs.oz.dwts.gr. 

(2)  185     2  19  20     (3)  16     4  18     6    (4)  172  11   19  22 

56     9  15     6              7     9  11   22             12     4  13  12 

1472  11     2  17          163     7  12  18       '      18     5  11  20 

385     0     ^5     /    .17     0  13     0  '       119  11  13  18 

1         10     Pl  ■   7  I*'* -. -— ..                n      0      ^   T^ 

.,  , .  ,,  ,     Am  901    ini'i'^^                010     0  90 

Ann  c>i  in      ft    T?    1«                

APOTHECARIES'  WEIGHT. 

fe    5  3B^r.        ife     3  3  9g-r.         ft     3  3  B^r. 

(2)    84  .7  6  0  12  (3)  18     0  1  0  12  (4)  182     3  10     0 

■  132    5  0  2     0       175  10  5  0  10          12     10  2  17 

16    2  2  2     8       472     3  1  2     3          17     2  4  2  15 

1427    6  7  0  19           0  11  7  2     0            0  10  2  1  19 

Id    0  6  1     9         ■ 

Ans.667    1   7  2     5Ans.212     5  1   1   11 

LONG  MEASURE. 

yd.  ft.  171.               L.  m.f,  p.  yd.  ft.  in.               L.  m.  f.  p.  yd.  ft. in. 
(2)     3  2  11    (3)172  2  3  19  2  2    4     (4)462  17  29  1110 
119              000  14  1   0    3              000110110 
20    8              0  12290010              4  1  2  28  1  2    9 
31  10              0040000              000  13  0  0    0 

627              00  0    032    3Ans.46703    140    5 

Ans.20  1     1  Ans.  173  1  4  23  210    6 

CLOTH  MEASURE. 

E.  E,  qr,  n,                               E,F.  qr,  n, 

(2)     72     3     2                          (3)       19     2     3 

536     2     1                                   728     1     2 

847     1     3                                   142     0     1 

1453     0     2                                   816     0     0 

41     2     0                                     32     1     2 

Ans.  2951    0    0                     Ans.  1739    0    0 

24                       canrouAD  addition 

, 

yd.  qr. 

(4)         19     2 

14     2 

32     0 

0     3 

142     3 

na.                       E. 
3                  (5) 
0 

o 

1 

2 

Fr. 

143 

17 

172 

182 
132 

72 

qr.  na, 

0  3 

2  2 

1  1 
1     3 

3  2 
1     1 

Ans.  210     0 

0 

720 

10 

A.  R.  P. 

(2)    487  2  17 

25  3  28 
e-V  0  32 
45  1   16  . 

26  0  29 

LAND  MEASURE. 

A.  r:  p. 

(3)  22  2     0 

700  3^27 

47  0     5 

39  0     0 

47  2  39 
0  3  28 

A 
(4) 

Ans 
( 

Ai 

A.  R.  P. 

(4)     132  3  25 

654  C   17 

462  3  25 

16  0     4 

1665  3  38 

Ans.  652  1     2 

Lns.  2931  3 '29 

Ans.  858  0  19 

hhd.  gal.  qt.  pt. 
(2)    385  42  3  1 
27  36  2  0 
132  17  0  0 
729  25  0  0 
163  47  2  1 

Ans.  1438  43  0  0 

T.     h.  gnl.qt.pt. 

862  10  10 
0  0  32  0  1 
0  0  37  2  0 
0  0  32  1  0 
0  2     0  0  1 

LIQUID  MEASURE. 

T.    h.  gal.  qt.pt. 

(3)    19   2    19   0   0 

45  0     Oil 

0  3  17  2  0 

0  0  21  0  1 

Ans.  65  1  58  0  0 

863  0  39  1   0 

DRY  MEASURE. 
B.  p.  qt.pt 
(3)  754  2  5  0 
469  0  2  0 
385  2  7  1 
375  0  0  1 
0  3  2  0 

B.  p.  qt.pt. 
(2)     47 '2  4  1 
635  0  3  0 
247  3  0  1 
285  0  2  0 
734  2  5  0 

B.p.  qt.pt, 

4)  144  3  2  1 

.0120 

0  0  3  1 

462  3  0  1 

72  0  5  1 

Ans.  1950  0  7  0 

Ans.  1985  1  1  0 

18.  680  0  fi  0 

COMPOUND  ADDITION. 

25 

TIME. 

F.  m.  w?.  6?. 

h.  m.  sec. 

F. 

m,  w,  d.  h.  m.  sec. 

(3) 

172  0  1  0 

4     0  62         (4) 

462 

4  0  0     5  37  24 

0  0  0  0 

0  34  18 

62 

0  0  0  11     0  24 

15  4  0  5 

3  27     0 

0 

0  15     0  13     0 

Ans 

0  0  13 

21  35  18 

0 

6  1  4  13   12  37 

187  4  3  2 

5  37  28       Ans 

524 

10  3  3     6     3  25 

MOTION,  OR  CIRCLE  MEASURE.                        | 

^g,'>    '      '' 

sig.'>   r 

It 

sig,  «     '      '' 

(2) 

2  7  32  16 

(3)  5  10  46 

38 

(4)  0     0  45     0 

0  5  27  24 

0  11  37 

18 

1     9     0  18 

1  6  17  13 

1     0  47 

12 

0  14  21  34 

0  7  38  24 

0     0     0 

18 

2     8  13  54 

4  5  42  19 

2     0     0 

52 

4     7  12  19 

1   15  12  23 
0  11   57  '^Q 

0     0  47  32 

Ans 

.  8  2  37  36 

Ans.  8  10  20  37 

Ans.  10  20  22 

10 

APPLICATION. 

$      ds. 

F.   qr. 

na. 

B,p,qt, 

fl) 

375     45 

(2)     57     2 

0 

(3)     2     2     0 

142     371 
1375     56| 

29     3 

2 

3     3     5 

45     1 

0 

3     1     1 

32     3 

38     2 

1 
0 

2     0     4 

Ans 

18f}4     38^ 

38     2 

0 

Ans.  113     2 

A,  n 

Ans.  242     1 

3 

F.    qr,  na. 

P. 

(4)     142     2 

0 

(5) 

15     3     0 

32     3 

12 

18     1     2 

108     3 

18 

Ans. 

25     3     2 

Ans.  284    0  30 

60     0     0 

26  COMPOUND  MULTIPLICATION. 

M.fur,  p.  B.  p,  qt, 
(6)  43  3  0  (7)  756  2  0 
29  0  34  756  2  0 
57  2  32  756  2  0 
12  3  18  854  0  6 
854  0  5 


Ans.  142  2  4 


Ans.  3977  3  2 


COMPOUND  MULTIPLICATION. 


EXAMPLES. 

FEDERAL  MONEY. 


$      ets.  g      cts.  m.  $      cLt. 

(4)     26     18|  (5)     100     40     4  (6)     66     18J 

6  10  9 


Ans.  157     12i       Ans.  1004    04     0        Ans.  505     68J 


$    da,  m.  $       ds. 

(7)     26     37     5  (8)     665     62^ 

8  12" 


Ans.  203     00     0  Ans.  6787     50  • 


ENGLISH  MONFV. 

£,     s.    d,  £  s,      d. 

(2)     14     6     OJ  (3)     111  11     101 

9  lO"' 


Ans.  128  14    2}  Ans.  1115     18     9 


COMPOUND  MULTIPLICATION.                         271 

£      8.    d.                                   £    a,    d, 
(4)       37     6     91                         (5)       66    ^8     7-J  . 

6"                                                 9 

Ans.  186  13  n\ 

Ans.  507  17     9|                j 

AVOIRDUPOIS  WEIGHT. 
T.cwt.  qr,  Ih,  oz,  dr.                     qr,  lb,  oz,  dr, 
(2)       6  14     2     7     5     2              (3)       3  16     7     8 
4                                          10 

Ans.  26  18     1     1     4     8 

Ans.  35  24  11     0 

CwL  qr,  lb. 

(4)         12     6 

10 

Cwt.  qr.  lb. 
(5)        4     3     17 

Ana.  15    2    4 

^.     TROY  \VI 
U),  oz.dwt.gr.           lb. 
(2)      43     0     8  10      (3)  113 
4 

Ans.  53     3     19 

:IGHT. 

oz.dwt.gr.        lb.  oz.  dwt. 
6     0     6     (4)  17     9  14 
6                       10 

Ans.  172     1  13  16  Ans.  681 

0     1  12  Ans.  178     1     0 

lbs.  oz.dvjt.gr. 
(5)      41     6  18     2 

lbs.  oz.  dwt.  gr. 
(6)      91     4  14  16 
8 

Ans.  291     0     6  14           Ans.  731     1  17     8 

APOTHECARIES'  WEIGHT. 
Ik    ^    3    B  gr.                         m    ^    Z    B  gr. 
(2)     63  10     0     2  12                 (3)     17     5     6     1     4 
9                                                   12 

Ans.  484     6     7     2     8 

Ans.  209     9     4     2     8      1 

-n .7--^ . . ^ r—T^, '! 

28 

(4) 
Ans. 

(2) 

Ans. 

(4) 
An. 

1 
(2) 

Ans. 
(5) 

Ai 

J 
(?)    1 

COMPOtlSD  MULTIPLICATION. 

Ife339                       m    ^    Z    B  gr. 

76     4     1     2    ..              (5)     95     1     2     1    11 
9                                                        11 

687     1     7     0 

Ans.  1046     2     3     2     1         11 

LONG  MEASURE. 
L,  J\l.fur,p.                         M,fur,p,yd,ft.  in, 
4     2     2  29                   (3)     18     3  20     1     2  10 
7                                                            5 

33     1     3     3 

Ans.  92     1  21     31  2    2 

6     40     7 
10 

M.fur.  p. 

(5)         44     6     20 

7 

3.  66     48     6 

Ans.  31^     5     20 

CLOTH  IVIEASURE. 
iJ.^.  qr.  na,              E,Fl.  qr,  na,          E,Fr,  qr.  na. 

37     4     2          (3)     18     0     3         (4)     14     1     3 
8                               12                                9 

63     1     0       Ans. 

217     4    0      Ans.  129     0     3 

Yds.  qr.  na. 
19     1     2 
5 

E.  E.  qr. 

(6)         56     3 
9 

18.  "96     3     2 

Ans.  609    2 

LAND  ISIEASURE. 
l.R.P.          A.R.P.        A.R.P.          A.R.P. 

9  3  20     (3)  10  0  33  ■  (4)  1  3  11      (5)  63  3  18 
6                        9                     10                       11 

Ans.  119  1  00  Ans.  91.  3 

17  Ans.  18  0  30  Ans.  702  1  38  1 

-7^-r— r^ '} 

COMPOUND   MULTIPLICATION.  29 

LIQUID  MEASURE. 
T,  hhd,  £^al.  qt,  pt.  P.  hhd.  gal,  qt,  pt. 

(2)     1     2    16    3     1  (3)     4     1   19     3     1 

10  5 


ins.  15 

2 

42  3 

0 

(4) 

T. 

3 

h.  gal.  qt. 

2  50     2 

8 

Ans. 

29 

2  26 

0 

Ans.  23    0  36     1     1 

H.  gal.  qt.  pt. 
(5)     4  41     0     1 
10 


Ans.  46  33     1     0 


DRY  MEASURE. 
Bu.pe.  qt.  pt.  Bu.  pe.  qt.  pt. 

(2)       13     3     2  (3)     110     3     0     2 

4  4 


Ans 

7 

2 

0  0 

(4) 

B. 

A4. 

^0 

qt.  pt. 

0  1 

7 

Ans. 

308 

0 

3  1 

Ans.  443 

0  4 

0 

(5) 

P. 

3 

qt. 
1 
9 

ns.  Bush. 

7  0 

1 

TIME.- 

Y.  m*  w.   d.   k.min.sec.  W.  d.  h. 

(2)      17     8     2     6     4  40  18  (3)     S     5  22 

6  12 


Ans.  106 

0 

1 

2 

4 

1 

48 

(4) 

F. 

7 

m. 
0 

w. 
4 

4 
0 

Ans. 

63 

10 

1 

1 

Ans.  46 

1 

0 

Y.  m. 

(5)   16  2 

w. 
0 

d. 
6 
8 

A.ns.  121  4 

2 

6 

TT*" 


30 

(2)  Multiply 

Ans.  1 

t 
(4)       44 

COMP(5UN] 

£     S.     d, 
^  37  10     6| 
6X 

a  MULT] 

RULE 

EXAMPL 

by  48 
:8=48 

56 
=56 

120 
=120 

Ai 

4 
.54 

PLICATION. 

2. 

ES. 

%     Cts.  7/1. 

(3)     66  37  5  by  36 
6X6=36 

225 

'f 

398  25^0 
6 

801 

r  0 

Ans.^2389  50  0 

cts, 

25 

m. 
3  by 
7X8= 

(5)     12     18J  by  96 
12K8=96 

309 

77 

I 
8 

146     25 
8 

Ans.  2478 

16 

8 

Ans.  1170     00 

(6)      45 

6 

d. 

9*  by 
12X10= 

£    s.     d. 
(7)     96  12     3|  by  144 
12X12=144 

544 

1 

6 
10 

1159     7     9 
12 

Ans.  5440 

15 

0 

IS.  13912  13     0 

A. 

(8)      47 

R, 

3 

P. 

20  by  5 
6X9= 

(9)     48     7  25  by  88 
11X8=88 

538     3  35 
8 

287 

1 

0 

9 

Ans.  2585 

1 

0 

Ans.  4307     7     0 

COMPOUND  MULTIPLICATION 

31 

0 

I 

lb. 

0)         56 

oz 
9 

.dr. 
6  by  fi 
12X7= 

4 
84 

681 

9 

0 

7 

\n^.  4772 

3 

0 

RULE  3, 

EXAMPLES. 

(2)  Multiply  7 

Cts. 

871 
11x4+3- 

(3] 

47 

28 

cts. 

68f 
11x6+2=68 

86 

62^ 
4 

■&5k 

Ans. 
(5) 

Ans 

315 

56» 
6 

346 
23 

50 
62| 

1893 
57 

371 
37| 

Ans.  370 
(4)         49 

l^ 

cts. 

75X3 

12 

1950 

75 

$ 
94 

18JX1 
10 

597 

00 

941 

'? 

4179 
149 

00 
25 

2825 
94 

62i 
18| 

Ans.  4328 

25 

;.  2919 

81J 

32 
(6) 

Ans. 
(8) 

Ans. 
(10) 

Ai 

COMPOUND  MU 

$     cts, 
42  31J-X3 
11 

LTIPLICA 

(7) 

Ans. 
(9) 

Ans 

(") 

Ans. 

noN. 

£ 

28 

*.  d. 
7  6iXl 
4 

465 

43J 
5 

113  10  2 

7 

2327 
126 

18| 
93J- 

794  11  2 
28  7  6J 

2454 

12^ 

822  18  81 

34 

s.    d. 
8  4|X1 
11 

Cwt. 
7 

(^r.  lb. 
3  22X1 
10 

378 

12  A\ 
6 

79 

1  24 
6 

2271 
34 

14  li 
8  4| 

397 

7 

1  8 

3  22 

2306 

2  6| 

5.  405 

1  2 

lbs 
12 

.  OS,  dwts, 
5     8X3 
12 

Jtf. 

4 

6  21X3 
12 

149 

4  16 
3 

67 

6  12 
7 

448 
37 

2  8 
4  4 

404 
14 

4  4 
3  23 

IS.  483 

G  12 

418 

7  27 

(2)  Multiply 
1 

COMlhJUND  MULTIPLICATION 

RULE  4. 

EXAMPLES, 

1     56^X6                     (3)     2 
10 

33 

Ct8. 

871X6 
10 

5     65X5 
10 

28 

75X7 
10 

15 

6     30 

4 

287 

50 
5 

626     00 

78     25 

9     39 

1437 

201 
17 

50 

25 
25 

AUB.  713     64 

Ans.  1656 

00 

(4)          4 

cts, 

31^X9 

10 

(5)      18 

Ci8. 

93JX7 
10 

43 

121X7 
10 

189 

371X5 
10^ 

431 

25 
6 

1893 

75 
4 

2587 

301 

38 

50 

86^ 

81| 

.    7575 
946 
132 

00 

871 

56| 

Ans.  2928 

18| 

Ans.  8654 

433 

34 
(6) 

Ans. 
(8) 

Ans 

25 

CO^irOUND 

cts. 

43JX9 

10 

MULTIPLICATION.                              1 

$     Cts.                   1 
(7)      0       1JX6              II 

II 

254 

371X7 
10 

0 

171X6 
10 

2543 

75 
8 

1 

75X2 
10 

20350 
1780 

228 

00 

621 

03| 

17 

35 
3 
1 

Ans.  39 

£ 

(9)      37 

50 

2 

00 
50 
00 
10^ 

65| 

s.    d. 
18     6{X5 
10 

223'59 

56J: 

10 

cU, 

161X9 

10 

101 

65X3 
10 

379 

6     21X7 
10 

1016 

50 

9 

87S2 

12     !• 
3 

9140 

304 

91 

50 

95 
481 

^               11377 

2654 
189 

16     3 
16     64 
12     7| 

.  9544 

93J 

'Ans.  14222 

5     3J 

£    s.    d, 
(10)      48  14     21x9 
10" 


COMPOUND  MUIiTirLICATION. 


36 


487 

2  IX 
10 

4871 

0  10 

4 

19484 

3896 

438 

3  4 

16  8 
7  101 

Ans.  23819 

7  101 

(12) 


£     8.    d, 

58     9     6fX6 
10 

584  15     71x9 

lo' 

5847  16     3 
3 

17543  8  9 
5263  0  71 
350  17  41 


Ans.  23157  6  9 


£,     s.     d, 
64  2  8X5 
10 


641  6 

6X 
10 

6413  6 

6 
5 

32066  13 

3206  13 

320  13 

4 
4 
4 

Ans.  35594  0 

0 

M,   /.  p. 
(13)   25  3  18X5 
10 


254  2  20X6 

lb 


2543 


1  0X2 
10 


25430  10  0 

5086  2  0 

1525  7  0 

127  1  10 

Ans.  32170  4  10 


36 

F. 

(14)         48 

COMPOUND  MTJLTIPLICA 

in.b.c.                        Yd.  gr.n. 
42x7      (15)2221X4 
10                           10 

rioN. 

Hhd.gal.qt. 
(16)  4  37  2by 4250 
10 

45  60  0X5 
10 

483  10  2X8 
10 

225  2  2 
10 

4838  10  2X5 
10 

2256  10X2 
10 

459  33  0X2 
10 

48388  10  2 
2 

22562  2  0 
3 

4595  15  0 
4 

96777 

24194 

3871 

338 

91 
51 
1  1 

82 
,    An 

67687  2  0 

4512  2  0 

90  10 

18380  GOO 
919    3  0 
229  48  0 

s.  72290    1  0  Ans 

.  19529  48  0 

Ans.125182 

02 

APPLICATION. 

gl.07        (3)    $5 
9 

.62J         (4)  gl.l2l 
12 

(1)   $12.50 

(2) 
Ans. 

s.    d, 

2    2  by 
7 

Ans.  62.50 

9.63        Ans.  67.47                   6.75   [1 

£ 

(5)          0 

63             (6)     3 

-X 

Ans.  27.00 

871  by  G  1 
8 

0  15     2 
9 

31 

00 
8 

Ans.  6  16     6 

Ans.  248 

00 

$ 

(7)          0 
1 

COMrOUND  MULTIPLICATIOrf, 

C«*.                           £    S,     d,                          $ 
15^X6        (8)    0     1     3             (9)      9 
10                                  12 

37 

ds. 

10X5 

10 

521 
10" 

0 

15 

0 
11 

91 

0X6 
10 

15 
0 

25 

911 

Ans.  8 

5 

0 

910 

0 
3 

acre  X  5 

^ 

A 

$ 
(11)    1 

Ans.  10 

161 

2730 

546 

45 

0 

0 
50 

£ 

(10)      0 

s.    d. 
9     6  per 
10 

n3.332i 

50 

ds. 

18|X7 

10 

le  cost. 

4 

15     0X2 
10 

11 

871X1 
10" 

47 

10     0 
3 

118 

75 

2 

142 
9 

2 

10     0 
10     0      . 

7     6 

237 

11 

8 

50 

871 

31J 

Ans.  154 

7     6 

ins.  257 

68|  prin 

IT 


38  COMPOUND  SUBTKACTIOI^. 

Again:     $\     37^X7 
10 


13 

75X1 
10 

137 

50 

2 

275 

13 

9 

00 
75 
621 

g298 

g257 

g40 

37»  sold  for. 
681  prime  cost. 

68J  gain. 

COMPOUND    SUBTRACTION. 

EXAMPLES. 

FEDERAL  MONEY. 

g  ds.m,  ^  cts,  $    cts^, 

(2)  From  24  60  7      (3)  60b  62^      (4)  110  ISf 

Take  19  30  0        :  U^s'  99  10| 


Ans.  5  30 

7 

(5) 

$  ds,  m. 

960  10  2 

9 

Ins 

. 960  09  3 

Ans.  5 

$ 
449 

1 

98  87^ 

(6) 

ds. 
621 
06| 

Ans. 

448 

55J 

Ans.  11  81 


$      ds. 
(7)  1866  00 


Ans.  1587  88| 


COMPOUND  SUBTRACTION. 

$      ds.                       $     els,  m. 
(8)      104     06*          (9)     4010     14  4         (1 
9J                    1011     12  5 

0) 
ns. 

7 
8 

$ 
400 

211 

3d 

cts, 
00 
121 

Ans.  103     961         Ans.  2999 

1  9         A 

188 

d, 
6 

H 

871 

ENGLISH  MONEY. 
£     s.    d,                                 £ 

(2)          47     6     7|                      (3)      419 
28     5  101                                 227 

Ans.  19     0     9J 

Ans.   191 

18 

8f 

£    s.    d, 
(4)          1000  11   113 
200     9     0 

£ 

(5)      1000 
60 

s, 
2 

7 

d. 

51 

Ans.  800    2  11| 

Ans.    939 

14 

n 

AVOIRDUPOIS  VVEIOHT. 
T,  cwt.  qr,  lb,  oz,  dr,                      cwt, 
(2)      18  16     1   16     9     2                 (3)      9 
0  19     3  20     0     6 

qr,  lb.  oz 
3  20     2 

2  23     5 

Ans.  17  16     1  24     8  12 

Ans.  9 

0  24  13 

T,  cwt,  qr,  lb, 
(4)       14  10     2  16 

0    0    0  n  ^g^^ 

Cwt 
(5)      400 

.  qr 
0 
3 

.lb. 

0 

14 

Ans.  14  10     2     5^^^^ 

Ans.  397 

0 

14 

TROY  WEIGHT. 

lb.  oz,  dwt.gr,                            lb.  oz. 

(2)      8     3     0     2                    (3)      106     0 

2     1  18     6                                10     6 

dwi 
0 

2 

15 

20 

Ans.  6     1     1  20 

Ans.  95     5 

17 

19 



40  COMPOUND  SUBTRACTION. 

lb.  oz.dwt,<^r.  11).  oz.dwt.gr, 

(4)      22     0  12    ^6  (3)       16     0     0     0 

14     6  110  12  11    10  11 


Ans.    7     6     16  Ans.    3    0     9  13 


APOTHECARIES'  WEIGHT. 

Ife339^.  fe53  ife33 

(2)      48     9  6   1     4  (3)  59     1  2  (4)    69     0     0 

1   10  0  2     8  63     7  5  14     9     1 


Ans.  46  11  5  1  16      Ans.     5     5  5        Ans.  54    2     7 


CLOTH  IVIEASURE. 

yd.  qr.nci.          yd.qr.na.     E.E.qr.na.  E.F.qr. 

(2)      950    12       (3)  49    0    2      (4)  66    4    0  (5)  44    1 

19    2    3             16    2    1            17    0    2  19    2 


Ans.  930   2    3   Ans.  32    2    1  Ans.  49    3    2   Ans.  24    2 


E.Fl.  qr.  Yd.  qr.  na.        Yd.  qr.  na, 

(6)     963     1       (7)   Bought  17     2     0    (0)  75     3     1 

174    2  Damarred        2    3     1  0    0     1 


Ans.  788    2        Remains  good  14    2    3  Ans.  75     3    0 


LpNG  MEASURE. 
Dcs:;.  m .  fur.  p.  M.fur.  p. 

(2)     20  50    4  20    (3)  Travels  first  day  43     5  20 
11   56     0  30  second  do"^.  32     4  00 


Ans.    8  54    3  30  Ans.  11     1  20  more. 


LAND  MEASURE. 

A.   R.   P.  A.  R.  P. 

(2)      502     2     10  (3)  69     1    ^3 

111     3       9  17     3     2 


Ans.  390     3       1  Ans.  51     2     1 


m 


COMPOUND  SUBTRACTION. 

^    LIQUID  MEASURE. 

T,  khd.  gaL  qt.  pL  Hhd,  gal, 

100  -1     19     ^     1                 (3)  2       0 

99     1     28     3     1  0     29 


41 


Ans. 


3     0 


Ans.  1     34 


(4)  From  I  pipe  of  wine,  which  is  126  ffals.,  subtract  93, 

leaves  33  gals,  of  wine.     Then  from  4  nhds.  of  brandy, 

subtract  29  gals.,  leaves  223  of  brandy.  Then  from2  bbls. 

of  beer,  subtract  1,  leaves  1  barrel,  which  is  31i  gals. 

Answer,  33  gals,  wine,  223  gals,  brandy,  31^  gals.  beer. 

DRY  MEASURE 

J5.  p.  qLpt.  B.  p.  qUpL  B.  p.  qt.pt. 

(2)      10    0    0    I       (3)    695    3    0    1       (5)  600    2    7    1 

9    2    6    1  589    3    5    0  146    3    2    1 


Ans. 


12    0      Ans.  105    3    3    1    Ans.  453    3    5    0 


TIME. 


H.  min,  sec. 

(2)  16     29     33 

7     36     44 


Y.    m.    Wr 

(3)      18     11     2 

9     10     3 


Ans.    8     52     49 


F.    m.   IV.  d, 

(4)      900     0     0     0 

111     6     2     6 


(5) 


Ans.  788     6     1     1 


Ans.    9 

0 

3 

y.  m. 
6     0 
1     1 

0 

1 

d.  h. 

0  0 

1  1 

s.  4  10 

2 

5  23 

MOTION,  OR  CIRCLE  MEASURE. 
sig.  ^    '      "  sig.  "^     '     "  sig,    **     '     " 

(2)      9     7  40     8      (3)  10  10  16  12       (4)  11'  2     5  14 
7     9  57  19  7  24  37  59     ;       .907  20 


Ans.   1  27  42  49    Ans.    2  15  38  13    Ans.  2     1  52  $A 


T>% 


APPLICATI(»r. 

(1)  6  feet  of  chain  at  $2,75 

per  foot  =  $16  59 
A  gold  ring  for  4  50 
Ear-rings  12  00 


42 


COMPOUND  SITBTR ACTION. 


g33  00  whole  amount. 
Ring    4  50  has  been  returned. 

To  receive  $28  50 


(2) 


2  doz.  pairs  at  75  cts. 

16  yds.  at  87|  — 

28  do.    at  22    — 

5  pair  at  31 J  — 

Amount 
Note  delivered 


Must  be  returned 

A,    R,  P. 

(.3)    1  St  tract  contains  690    2  16 

2d     do.       do.        400     0  0 

3d     do.       do.          63     3  21 

4th  do.       do.          63     3  24 


$  cts. 

:7=    18,  00 

=r=    14  00 

rrr      6  16 


1 

56J 

39 
50 

72| 
00 

10 

27J 

£  s.  d. 

(4)     55  6  7 

41  4  6 

75  0  0 


Collected  171  11     1 

In  the  whole  1218     1     24  Lost    40     6     0 

Sold  200    0    00  

I  have  131     5     1 

Remains 


1018     1     24 


Bu,p. 
(5)  Bought  400  3  of  wheat, 
Sold      225  1      do. 

Remaining  175  2 


Bu.  p.  Bit.  p. 

160  Oof  rye,  150  2  of  oats, 

37  2      do.  78  3      do. 

122  2  71  3 


COMPOUND   DIVISION.  43 

COMPOUND  DIVISION. 

EXAMPLES. 

$     cls,  $  '  cts,  $    ch. 

(3)  3)366  18 J    (4)  6)384  S^         (5)  8)496  75 

Ans.  64  141-f  2   Ans.  62  09|-f  4 


tf  cts*  ^  cts*  ^      cts, 

(6)  9)587  68J    (7)  11)976  43J   (8)  12)1979  331 

Ang.  65  293-f  4   Ans.  88  76^-f  9   Ans.  164  94-J-f  4 


£      s.  d.  £     s,     d. 

(9)         3)560     9  7  (10)         5)475  19  •9J 

Ans.  186  16  6J-f  1  Ans.  05     3  ll^J-fl 

£     ,9.  d,  £     s.  d, 

(11)       8)596  15  61  (12)       12)756     4  llj 

Ans.    74  11  ll|-f2 


Cwt,  qr,  lb,  ,        '    Cwf,  qr,  lb.  Yds.  qr.  nn, 

(13)5)45     3'  27     (14)  9)10     0  \b       (13)  7)44     J     2    ■ 

Ans.    9     0  22+1  Ans.    1     0  14-f-l    Ans.  6     1     l-f3 

Yds,  qr,  na.  M.  fur,  p,  JSl.  fur,  p, 

(16)11)56     3     3  (17)  12)105     5  22   (18)  6)45'   7  18 

Ans.    5     0    2-f9     Ans.  8     6  18+6  Ans.  7    5     9+4 


When  the  divisor  exceeds  12,  but  is  the  exact  product 
of  any  two  figures  in  the  multiplication  table. 

$cts.m.  $cts,m. 

(19)6)45  66  5  ;(20)  4)98  77  8 

6l7]r0+5  ^^^    11)5^+2  ^^^^ 

Ans.     126  8+2x0+5=17    Ans.  2  24  4+10x4+2=42 


44  COMPOUND  DIVISION. 

^cis.m,  $  cts, 

(21)12)77  87  5  (22)  12)288  68| 

8)6  48  9+7  9)24  05l-fl 

Rem. Rem. 

Ans.    0  81  l+lXl2+7=19An».2  67|-f  lXl2-f  1=13 


ds.  m. 
(23)         12)^6  37  5 

11)41  36  4+7 

Ans.    3  76  0+4x12+7=55  Rem. 


£    s.     d. 
(24)         4)87  19     44 

8)21   19  10+2 

Ans.    2  14  11  +  6x4+2=2/ qrs.r=:J+2  Rem. 


£    s.    d.  £    8,    d. 

(25)3)55    4'7|  (26)8)97  15    6} 

7)18    8    21+1  7)12    4    5}+l 

. 1  Rem. ; Rem. 

Ans.   2  12    7+6x3+1=19  Ans.  1  14  11+1x8+1=9 


H}id.gal.  qt.  JThi.gaX.  qU 

(27)7)44  28  2  (28)  12)150  47  3 

9)622042  10)12351+11 

Rem.         Rem. 

Ans.  0441  +  7X7+2=51     Ans.  1  160  +  5x12+11=71 


COMPOUND  DIVISION.                                  45 

When  the  divisor  exceeds  12,  and  is  not  the  product 
of  any  two  figures  in  the  multiplication  table. 

^  cts.  ^  cts,  m, 
(31)78)196  75(2  52  2  An 3. 
156 

$  cts,  $cts,m, 
(32)  97)496  871(5  12  2 
485 

78)4075(52  cts. 
3900 

97)1187(12  cts. 
97 

175 

217 

156       ' 

194 

78)190(2  mills. 
156 

23 
10 

Rem.    34 

97)235(2  mills.   ] 
194 

41  Rem. 

g    cts,  $Ct9, 
(38)123)376  811(3  06|    An? 
369 

£  s,  d,£  s.  d. 
.(34)87)44  7  6(0  10  2\  Ans. 
20 

123)781(6  cts. 
738 

87)887(10  shillings. 
87 

43 

17 

4 

12 

123)172(1 
123 

87)210(2  pence. 
174 

49  Rem. 

36 

4 

S7)144(1  farthing. 
87 

57  Rem. 

46 

COMPOUND  DIVISION. 

£       »,    d,£   f.    d. 

(35) 

148)156     15    8|(1     1    2J  nearly,  Ans. 
148 

8 

20 

148)175(1  shilling. 
148 

27 
12 

148)382(2  pence. 

296 

36 
4 

147 
148 

PRACTICAL  EXAMPLEg, 

$ 

ds. 

«»•                                    i!  dt,  t  di. 

(1)     6)47 

87  5                       •   (2)  112)64  81}(o  57j  Ans.  || 





-                                          100 

*P_ 

97 

9+1                                   

-                                   112)6481(57  ct«» 

Ans.  1 

99 

4-f3x6-f.l=:l^Eem.    560 

881 

784 

97 

4 

U2)389(S 

336 

43  Rem. 

C03tP0Uril>  DIVIBION. 


47 


(3)  72)56  25(0  78  1  An&. 
100 


$   cts.$ct8.m. 
(4)  63)125  00(1  98  4  Ans. 
63 


72)5625(78 

Ct8» 

63)6200(98  cts. 

504 

567 

685 

530 

576 

504 

9 

26 

10 

10 

72)90(1 

mill. 

63)260(4  miUs 

72 

252 

18  Rem.  8  Rem. 


£   s.  d. 
(5)     4)18  17  6 

Ans.  4  14  4| 


£    s.     d,  £  s.  <?. 
(7)       1000)576  18     9^(0  11  4|  Ans 
20 


1000)11358(11  shillings. 
1000 


$     cts,   g  cts.  

(6)  125)1875  81 1-(15  00^  Ans.   1358 
125  1000 

625 
625 

125)00081(00  cts. 
4 

125)325(2  qra.  305 

250  4 


358 
12 

1000)4305(4  pence. 
4000 


75  R6m.  1000)1222(1  farthing. 

1000 

222  Rem. 


48 

REDUCTION. 

Gal.qt.pLG 
(8)  89)150  2  1(1 
89 

,qtpL                         a  I 
2  1  Ans.      (9)  19)9 
4 

jrJb.C.qr.lb. 

I  25(0  1  27  Ans. 

61 

4 

19)37(1 
19 

qr. 

89)246(2  quarts. 
178 

18 

28 

68 

149 

o 

38 

89)137( 
89 

I  pint. 

19)529(27  lbs. 
38 

48: 

aip. 

149 
133 

16  Rem. 

*»©®©M^ 

REDUCTION. 

FEDERAL  MONEY. 

EXAMPLES. 

0)     fo 

100 

(2) 

$ 
25 
100 

(3)     387 

100 

(4)     25 

4 

Ans.  1000 

Ans. 

2500 

Ans.  38700 

Ans.  100  fourths. 

REDUCTION.  49 

cts.  CiSt  ^ 

(5)      60  (6)     150  (7)     50 

2  ,3  100 

Ans.IOO  halves,      Ans.  45QthiTds»  5000 


(8)      25  (9)     275 

100  100 


Ans/ 10000  halves. 


2500  27500  (10)     10 

.3  4  10 


Ans>  7500thir(ls.  Ans.  110000  qrs.        Ans.  100  dimes. 


(tl)  220 

10 

'  2200  dimes. 
10 


22000  cts. 
10 


Ans.  220000  mills. 


JSTote. — When  more  than  one  denomination  is  given 
to  be  reduced. 

$   cts,  $  cts,  $    cts, 

(1)    15  15           (2)  2  25  (3)     17  18f 

100  100  100 

Ans.  1515  cts.  225  cts.  1718  cts. 
4  4 

Ans.  900  4ths.  Ans.  6875  4tlis. 


50 


REDUCTION. 


$  cts. 
(4)     13  27,J 
100 


%       Ct8, 

(5)  426  881 
100 


1327 
3 


42688 
2 


Ans.  3982  thifds. 


Ans.  85377  halves. 


ENGLISH  MONEY. 


£ 

364 
20 


70 
12 


(5)  12 
4 


(2)   364      (3)  20      (4) 
20         12 

Ans.  7280  s.     Ans.  240  df.   Ans.  840  d.     Ans.  48  qrs. 


d.  £  s,d.  £    s,  d,  £  8.  d. 

(6)  26   (8)  18  12  7   (9)  105  13  91  (10)  36  19  7J 


Ans.  104  qrs. 


20 

372 
12 


Ans.  4471  (/. 


20 

2113 
12 

25365 
4 


20 

739 
12 

8875 
4 


Ans.  101462    Ans.  35503  qrs. 


Cents  to  Pence. 


(2) 


cts, 
36975 
9 


(3)      57697 
9 


10)332775 
Ans.    332771  (f. 


10)519273 
Ans.    51927|-f£?. 


EEDUCTION.                                        51 

(2)          4590 
10 

Fence  to  Cent^, 

d, 

(3)      76975 
^0 

9)45900 

9)769750 

Ans.    blOQds, 

AVOl 
Cwt, 
(2)      260             (3) 
4 

Ans.  85527^5.  1  m,+l 

RDUPOIS  WEIGHT. 

qr,                   lb,                   oz, 
36             (4)     17             (5)  20 
28                      16                     16 

Aas.  1040  qrs. 

Ans. 

288                    102      .             120 
72                      17                    20 

1008/6*.  Ans.  272o5r.  Ans.320rfr. 

T,  cwt,  qr, 
(6)          5     12     2 
20 

Qr.  lb,    oz, 

(7)         2     25     10 
28 

112 
4 

21 
6 

Ans.  450  qrs. 

81  lbs. 
16 

486 
82 

1306  ounces. 
16 

7836 
1306 

Ana.  20896  drams. 

52 

KEDXTCTION. 

APOTHECARIES*  WEIGHT. 

3 

(2)     72 
8 

ft                          f^     i    3    Bgr. 
(3)     10                 (4)     15     9     4     2  17 
12                          12 

Ans.  576  drams.        120  ozs. 
8 

189  oz. 
8 

960  drs. 
3 

1516  drs. 
3 

2880  scru. 
20 

4550  scni. 
20 

Ans.  57600  grs.  Ans. 

91017  grs. 

CLOTH  MEASURE.                                    | 

Yds. 
(2)      36 
4 

E.E. 

(3)     20 
5 

E.Fl. 

(4)     16 
3 

Ans.  144  qrs. 

Ans.  100  qrs. 

48  qrs. 
4 

Ans.  192  na. 

E.FL  qrs. 
(5)      5     2 
3 

E.Fr.  qr. 

(6)      37     2 
5 

Yds.  qrs.  na. 
(7)      19     2     1 
4 

Ans.  17  qrs. 

Ans.  187  qrs. 

78 
4 

Ans.  313  na. 

KEDUCTION. 

53 

DRY  MEASURE. 

Pe. 

Bu, 

Bu. 

m 

32 
8 

(3) 

7 
4 

(4)      12 
4 

Ans. 

256  qts. 

Ans. 

28  pe. 

48 

8 

384 

2 

Ans.  768  pts. 

(5) 

Bu,  pe, 
14     0 
4 

56 
8 

qt, 
3 

(6) 

Bu*  pe,  qt,  pt, 
24     1     2     1 
4 

97 
8 

Ans.   451  qts. 

778 

2 

Ans.  1551  pts. 

LAND  MEASURE. 

A. 

^.  12.   P. 

(2) 

132 
4 

528 

.(3) 

54     3     23 
4 

219 

Ans. 

40 

Ans. 

40 
8783 

21120  p. 

fe^-~ 

54 

REDUCTION. 
SQUARE  MEASURE. 

Sq,  yds.                           Sq.yds.  s,ft.  s.in.                I 

(2) 

120                             (3)      29     2     102                  1 

9                                         9 

1080                                     263 

144                                     144 

4320                                   1054 

4320                                   1052 

Ans 

1080                                     264 

.  155520  sq,in.           Ans.  37^74  sq,  in. 

LIQUID  ]VIEASURE. 

Gals.              Hhds                 Gals. 

Tims. 

(2) 

28              (3)     5              (4)     110 

(5)     6 

4                    63                          4 

4 

Ans. 

\\2qfs.  Ans.  315^a7s.             440 

24 

^ 

63 

Ans.  880  p/5. 

72 

144 

Wids.  gals.  qts.               Gals.  qts. 

(6) 

7     41     2             (7)     47     2 

1512 

63                                     4 

4 

22                                  190 

6048 

46                                        2 

2 

482                    Ans.  380^^5.        Ans. 

12096  |)f« 

4                                

Ans.  1930  qts. 

' 

REDUCTION.  55 

Hhs.  gals.  qts.            Tvnskhds.gals.  Tun.hhd.gal.qt.pt. 

(8)      4     0     3     (9)    19     0     27  (10)  5     1   15     1     1 

63                            4  4 


252 
4 

76  hhds.               21 
63                         63 

1011 
2 

235                          68 
458                          127 

Us.  2022  pts. 

4815                        1338 
4                              4 

Ans. 

19260  (?f.9.                 5353 

2 

Ans.  10707  ;?f*. 

LONG  MEASURE. 

Yds, 
(2)     48 
3 

(3) 

Po.               Fur.               Miles* 
27             (4)     18             (5)     34 
b\                     40                      8 

Ans.  144/^ 

135          Ans.  720|>o.  Ans.272/wr. 
131                  _ 

Ans. 

1481  yds. 

L.  M.  M. 

(6)      108  ^  (7)     17  (8)      20 

3  320  p.~l  on.  1760  yds,=l  m. 

Ans.  324  vi.               340                Ans.  35200  yds. 
— «  51  

Ans.  5440^0. 


56 

BEDUCTION. 

X. 

FL  in. 

Yds.  ft. 

(9) 

6 
3 

(10) 

14  9 
12 

(11)  37  1 
3 

18 

Ans. 

177  m. 

Ans.  112/jf. 

8 

Fur,  po. 

144 
40 

(12)   112  29 
40 

5760 

^)4509 

^ 

28800 

22545 

2880 

2254^ 
Ans.  247991 

yds. 

31680 

3 

L,  m.fur 
(14)  2  1  3 

.po.  yds. ft.  in. 
16  3  2  10 

95040 

Ans. 

12 

n. 

3 
7 

1140480 i 

8 

59 
40 

(13) 
Ans. 

M.  fur, 
450  6 
8 

po. 
32 

3606 
40 

1)2376 

144212  po. 

11883 

1188 

13071 

^ 

3 

39215 

Ai 

12 

IS.  470590  in. 

REDUCTION. 

57 

TROY  WEIGHT 

(2)  116 
20 

lb.                 oz.  dwt. 
(3)  25    (4)  29  16 
12        20 

lb.oz.dwt.gr. 
(5)  19  11  14  21 
12 

Ans.  2320  dwt.    300   Ans.  596  dwt. 
20      

239 
20 

Ans. 

6000 
24 

4794 
'24 

24000 
12000 

19177 
9590 

144000  g-^-.       Ans. 

115077  ^r. 

TIME. 

(1)  30 

60 

hrs. 
60 

yrs. 
(3)   12 
12 

Ans.  1600 

s.             Ans.  720  w. 

Ans.  144  m. 

(4) 

d.  kr>  min. 
3  5  29 
24 

17 

6 

77 
60 

Ans.  4649  -min. 

68  EEDUCTION. 

MOTION,  OR  CIRCLE  MEASURE. 

(1)       24          (2)     4*        (3)     11*12  (4)4  3  18  27 

60                  30                    30  30 

Ans.  1440 '             120      Ans.  342  123 
60             60 

7200  7398 

60  60 


Ans.  432000  Ans.  443907" 


PROMISCUOUS  EXAMPLES. 

^  Fur,  Days.  H.cls. 

(1)      35         (2)    8)98  (3)  7)365  (4)  2)84 

100  —  — 

Ans.  12  m.  2/i/r.  Ans.  52 1/?.  1  d,  Ans.  42  cts. 

Ans.  3600  cts,        —  —  — 


TunscwU  R,  S,  P. 

(5)      8  15         (6)    63      (7)    2I0)15|7     (8)  4)175 

20  40  

,  Ans.  £7  17*.    Ans.  43  6«.  Sjjc. 

Ans.l75ctt?f.  Ans.2520 59. 2>cr.    — 


cts,  Pts,  Sec,      Hhd.gcd, 

(9)  100)76|42       (10)2)103         (11)  6|0)72|0     (12)733 

Ans.  J576  42  c^.  Ans.  51  qts,  Ipt,  Ans.  12  mm.  — 

45 

Ans.  474  gal. 


REDUCTION.  69 

Qrs.  Dwis,  S. 

(13)  5)100  (14)  210)10|8  (15)  2|0)25|0 

Ans.  20  E.  E.  Ans.  5  oz.  8  dwt     Ans.  £12  10*. 


3  s,d.  Days,             Qrs, 

(16)      7  (17)    8  8  (18)  7)203         (19)  16 

3  12                           4 

—                Ans.  29  w.           — 

Ans.  21  9  Ans.  104  d?.  —     '  Ans.  64  im, 


drs,  S,  Thins, 

(20)     16)74(4oz.l0<ir*.  Ans.      (21)13  (22)20 
64                                                4  20 

10  Ans.  threepences  52  Ans.  400  cwt. 


Qrs,                      Gal.  qt,  pL  M,fur. 

(23)     5)81                 (24)     21     3  1             (25)     3     1 

—  4  8 
Ans.  IftjE.Fr.  l^r.      —  — 

—  87  Ans.  25/wr. 

2  — 

Ans.  XlSpts. 


Cts,                       Days,  Cts, 

(26)     1|00)12135                  (27)     3  (28)     121 

24  4 

Ans.  $12  35  cts.  —  

72  Ans.  484  qrs. 

60  

Ans.  4320  m. 


60 


REDUCTION, 


lbs,  Qrs,                        Dwts, 

(29)       13  (30)  3)154            (31)  210)246|1 

16  

—  Ans.  51 E.  FL  1  qr,  12)123+ 1  dwU 

78  —  


13 

208 
16 

208 

Ans.  3328  drs. 

Yd,  qr.  na, 
(32)      12     2     1 
4 

50 

4 

Ans.  201  na. 


lbs,  oz, 
(34)        725     6 
16 

4356 

725 


Ans.  10 lb,3oz.  Idiot 


11606 
16 

G9636 
11 606 

Ans.  185696  drs. 


Gals. 
(33)  63)584621(4)9279 

567  

Ans.  2319  L  Zhhds.  Ug, 

176  

126 

502 

441 

611 
567 

44  gals. 

lbs.  qrs» 
(35)     28)27552(4)984 

252  

246  cwt.  Ans. 

235       

224 

112 
112 


SIN6L£  RULE  OF  THREE.  61 

£    s.  d.                      Days.  £    s,    d. 

(36)      5     4  6}         (37)     7)763             (38)    83  10     7 

i^O  20 

—  Ans.  109  ly.               

104  1710 

12  12 


1251                                             Ans.  20521  d. 
4 

Ans.  5017/i/r. 

Ors,  Q?.?. 

(3y)        ^10)122|0  (40)     5)27 

3)61  Ans.    5E.E,2qrs, 

Ans.  20  3  19 

Pts,  per. 

(41)         2)1357  (42)     4|0)865|4 

8)678+ 1  pL  4)216-1-1 4per. 

4)84+6  qis.  Ans.  54  a.  0  r.  lAp. 

Ans.  21  6w.  Op.  6  qts,  1  pL 

SINGLE  RULE  OF  THREE. 

EXAIVIPLES. 

lbs.  lbs.  cts.  ds. 
(3)  State  the  question  thus :  As  2 :  8  : :  60  :  200  Ans. 
For  50x8=400-^2=200  cts. 


62  SINGLE  RULE  OP  TUEE13. 

/6.  lbs.   cts,  cts» 

(4)  As  1  :  5  :  :  12  :  60 

For  12X  5=60-rl=  60  cU,  Ans, 
yds.  yd,       cts,      cts. 

(5)  As  10  :   1   :  :   650  :   55 

For  650x1=550  which -M0=:56d^.  Ans. 
lbs,     lbs.        cts,       ^  ct^, 

(6)  As  7  ;   122  :  :  87-|  :   15  25 

For  87^X  122=10675  which  -r-7=gl5  25  cts.  Ans. 
bu,     bu,         cts,       §    cts. 

(7)  As  1   :  209  :  :   72  :   150  48 

For  72X209=15048  which  -M=gl50  48  cts.  Ans, 
lbs.  lb.       cts.     cts, 

(8)  As  5  :   1   :  :   55  :   11 

For  55X1=55  which  --5=11  cts.  Ans. 
yd.  yds.       $cts,      $  cts, 

(9)  As  1   :   18   :  :  4  25  :   76   50 

For  425X  18=7650  which  -hl=$76  50  cts,  Ans. 
lbs.    lb,        ^  cts.      cts,     ' 

(10)  As  76   :   1    :  :  24  32  :   32 

For  2432 X  1=2432  which  —76=32  ds.  Ans. 
bu,  bu.       ^  cts,    cts.  m. 

(11)  As  8,:   1   ::   3  94  :   49  2+4 

For  394X  1=394  which  —8=49  cts,  2  m.-f  4  Ans. 

lb.     lbs,      cts,      $  cts. 

(12)  As  1   :   57  :  :   7|  :  4  27| 

For  7^X57=42n  which*'~l=^4  27}  ets,  Ans. 
bu,     Ini,        ds,       ^    cts, 

(13)  As  1    :   243  :  :   45  :    109  35 

For  45X243=10935  which -f- 1=^109  35  ds.  Ans. 


lb,       lbs.       $  cti.         $  cts. 

(14)  As  1    :    147  :  :   1    12;i   :    165  37^  Ans. 

For  112^X147=165374^  wliich  l-l=gl 65,37^  c/5. 

lb.      lbs.       ds.      jJ5   cfs. 

(15)  As  1    :   869  :  :  4^  :   39   10^ 

For  4^X869=3910^  which" —  1=^39  10^  cts,  Ans. 


SINGLE  EULB  OF  TKKEE,  ()3 

yds,     yd,        $  cis.      f  cU. 

(16)  As  24  :   1   :  :   125  24  :  /I  21-f  20        An&. 

For  12524 X  1  —  12524  which  -i-24=:g5  21  ct?.-f  20 
C.    /6.        ^  0^5.     cts.m, 

(17)  As  1   :   1  :;   11  50  :   10  S-f-TO. 

Zi5.      lb.         ^  c^*.      C^'.  J». 
Or,  as  112  :  1  ::  11   50  :  10  2-f  76  Ans. 

For  1150x1—1150  which  -M12:=cl0  cU,  2  m.-f  76 
/?;.     ^*.       cU,     ^  cf^. 

(18)  Aa   1   :  218  :  :   7  :   15  26 

For  7X218=cl526  which  ~-f=gl5  26  <?^.  Ans. 
bu,    btt,       £,    8,       8.  d» 

(19)  As  57  :   1   :  :  SO  10  :   10  8|-f  S9 

Or,  as  57  :   1   :  :  610  :   10  8|-f 
For  610X  1=610  which  -7-57=105.  Sl-d.^Sd  Ans. 
oz.  Ibs.oz.      cts,      §  ci^, 

(20)  As  1  ;  3  5  :  :  72  :  29  52 

o^.     oar,       c^,      ^  cdj?. 
Or,  as  1  :  41  :  :  72  :  29  52 
For  72X41=2952  which -r  1=^29  52  c^.  Ans. 
lb,     lbs,         cU,     g  ctt, 

(21)  As  1   :   135  :  :   10  :   13  50 

For  lOx  135=1350  which  --1=^13  60  cU.  Ans, 
C.      T,  C,      £  s.  d.       £     8.  d, 

(22)  As  2  :   15  3  :  :   7  12  C  ;   1155  3  9 

C,       C,  d.  £    8,  d. 

Or,  as  2  :  303  :  :   1830  :   1155  3  9 
For    1830X303=554490    which    ~2=277245f?.= 
£1155  3^.  9d.  Ans. 
8,   d,      £  8.  d,     gaL  gals, 

(23)  As  4  10  :  54  7  6  :  :   1   :  225 

^.  d,        gal,  gah. 

Or,  as  58  :   13050  :  :   1  t  225 
For  1 X  13050=13050  which  -^58=225  gal^,  Ans. 
M.     to.         els,        §  cts, 
{9-<)  As  1   :  52  :  :  250  :   130  00 

For  250X52=13000  which  -^1=^130  00  rfg.  Ans. 


i]^  SINGLE  IIULE  OF  THKEE. 

J.    A,  R.  P.        $  ds.       $     cts. 

(25)  As  1   ;  34  1   17  :  :  4:2  ^25  :   1451   55-^25 

P.         P.  ^  cis.        $     cts. 

Or,  as  160  :   5497  :  :  42  25  :   1451   55+25 
For  4225  X54a7F=232 24825   which    -T-160=gl451 
55  cts. +25  Ms. 

gals.  gal.     jj    s.       s. 

(26)  As  131  :   1   :  :  Qb  10  :  10 

gals.    s^al.         s.        s. 
Or,  as  131  :^1   ::   1310  :  10 
For  1310X  1—1310  which  -M31==105.  Ans. 
$  $  T.  T.hhd.gaLqt.pt. 

(27)  As  754  :   1754  :  :   1   :  2     I   19     0     1 

For   1X1754=1754  wliich  -r  754=2  21 M  AW.  1 9 
gal,  0  qt.  1  pt.  Ans. 

s.  d.      £    8.       yds.  yds. 

(28)  As  18  8  :  36   16  :  :  7  :  276 

d.  d.         yds.  yds. 

Or,  as  224  :  8835>  :  :   7  :  276 
For  8832  X  7=61824  which  -^ 224=276  yds.  Ans. 
Ih.  cwt.  qrs.  lbs.      cts.       ^  cts.  m, 

(29)  As  1   :  5     2     17  ;  :  91  :  60  13  5 

lb.      lbs.       cts.      §  cts.  in. 
Or,  as  1   :  633  :  :  91  :  60  13  5 
For9lX  633=6013^  which -Hl=^60  13c^5.57n.  Ans. 
its.       jJ  lb.    Ibs.fiz.  dr. 

(30)  As   114  :   354  :  :    1    :   310  8  6+84 

For  1X35400=35400  which  -M  14=310/6*.  8  or. 
6  Jr. +  84  Ans. 

£,  s.        £,  s.     skeins,  skcms. 

(31)  As  2  10  :   105  3  :  :    100  :   4206 

s.         s.         skeins,  skeins. 
Or,  as  50  :  2103  :  :   100  :  4206 
For  100X2103=210300  which  -r  50=4206  sk.  Aus. 
yds.  yd.  '      ^     cts.     j^  cts.  m. 

(32)  As  39   :    1    :  :   350  38   :   8  08  4+         Ans. 

For  35038 X  1=35038  which  -r39=,^8  ^cts.Am. 


SINGLE  RULE  OP  THREE.  65 

get  Is,  qts,  gals.  qt.  pt.  gals.  qi8.  pt. 
(33)  ei^gah.^Ql     2+62     1     1  =  123     3     1 
pL    gals,  qts.pt.       ds.        ^     cts. 
Then  as  1  :   123     3     1  :  :  37|  :  371  62i 

pt.  pis.  cts.  ^  cfe. 
Or,  as  1  :  991  ::  37i  :  371  62^ 
For37iX  991=^371621  which -rl^^3716?id*.Ans. 

bu.    bu.     hu, 
^34)  75+87=162 

hu.  hu.  cts.  fi  cts. 
Then  as  1  :  162  :  :  52  :  B4  24 
For  52X162=8424  which -r  1=^84  24  ds.  Ans. 

(35)  1  year  equals  365  days. 

day.  days.        cts.         ^   cts. 
Then  as  1   :  365  :  :   1871  :   684  37X 
For  187^X365=384371 'which  +1=^684  37|  d*. 
the  sum  he  spends  in  a  year ;  his  income  yearly 
is  ^1022—^684  37|  c^.=|337  621  ds.  Ans. 

cwt.  cwt.qrs.  lb.       ^  cts.      ^  cts. 

(36)  As  1  :  4     3     24  :  :  2  10  :   10  42| 

lbs.      lbs.        cts.        ^  cts. 
Or,  as  112  ;  556  :  :  210  :   10  421  price  of  stove. 
For  210X556=110760  which  ~n2=JlO  42^  cts. 

price  of  stove. 
Then  27  Ws.  X  18j  c/^.=g5  06 j-  cts.  amount  of  pipe, 

and  50  c^A'.x2=gl.OO  nrice  of  2  elbowi5. 

+  ^10  421  ctv,  price  of  stove. 

4-^  ^  06}-  cts.  do.  pipe- 

-fg  1  00  c^.    do.         elbows, 

$16  48 J  Ans. 

(37)  14  pair  X  2=28  single  shutters,  which    X  8^=243 

whole  number  of  sheets  used. 
sheet  sheets,     cts.        $  cts. 
Then  as  1  :  243  :  .  Ill  :  27  37 
For  243X  11^=2737  which  +1=^27  37  cts.  Ans. 

-—-/     [         ■  ■        ■      J I         -J ■      I •! 


6G  SINGLE  RULE  OF  THREE. 

(38)  If  45  men  eat  1  lb.  per  day  each,  they  will  alto- 
gether eat  45  lbs.  in  a  day. 

lbs,      lbs»         (1.     w,  d. 
Then  as  45  :  45G0  : :   1   :   14  2 
For  1X4500=4500  which  -^45=^100  d,^\ 4  ^veeJi's 
2  days,  Ans. 

A.R,    A.R,P,      hu.pe,     hu,    pe,qts,pt. 

(39)  As  12  2  ;  37  3  5  :  :  443  3  :   1341     0     7     1 

P.         P.  pe,         hu,    jte.  qlft,  pL 

Or,  as  2000  :  6045  :  :  1775  :  1341     0     7     1 
For  1775x6045=10729875  which -^2000=1341  hu. 
0  pc,  7  qts,  1  pt,  Ans. 

$    ds, 

(40)  Amount  paid  for  the  sugar  204  00 

carriage     15  75 
storage     IB  31} 
and  would  fjain    57  00 


g295  00}    the    sum    the 

whole  must  sell  for. 

Cqrs,  C,         $     cts,       $  cf.s,m. 
Then  as  27  2  :   1   :  :  205  0G|  :   10  72  9-fCO 

qrs»    qrs,         cts.  $  cts.vi. 

Or,  as  110  :  4  :  :  29506}  :   10  72  9-f  60 
For  29506}X 4=118025  which  —110=^10  '72  cis. 
9  7«.-f60  Ans. 

(41)  To  find  how  much  per  cent,  he  can  ijay. 
$      cts,        $     cts,  $         % 

As  18284  40  :  9142  20  :  :  100  :  50  per  cent. 
For  100x914220=91422000   which    -M828440= 

50  Ans.  the  first. 
To  find  what  the  creditor  is  to  receive. 

$       cts.         $    cts.         $         $ 
As  18284  40  :  9142  20  :  :  472  ':  236 
For  472X914220=431511840  which  —182^440= 
p2e  Ans. 


SINGLE  RULE  OF  THREE.  iSJ 

INXmSE  PROPORTION. 
m.    VI. .      d.     d. 

(42)  As  12  :   6  ::   18  :   9 

For  I8x 6r=l08  wlxich  -f- 12=9  days.  Ans. 

m.      Tiu        d,       dk   h, 

(43)  As  18  ;   12  ::  20  :   13  4 

For  20  X  1 2=240  which  -^18=13  days  4  hours.  Ans. 
d,     d,       m,     m. 

(44)  As  4  :  24  :  :   8  :  48 

For  8  X  24=  1 92  which  -r  8=48  men,  Ans. 
nu     m.         d.     d. 

(45)  As  48  :   12  :  :  24  :   6 

For  24X  12=288  which  —43=6  days.  Ans. 
h.       h.       d.     (/.  k. 

(46)  As  15  :   11   :  :  5  :  3  8 

For  5X  11=55  which  -rl5=3  days  10  hmirs.  Ans. 
ft.  in.  ft.  in.       ft.     yds. ft.  in. 

(47)  As  2  3  :   30  6  :  :   48  :  216  2  8 

in.      in.         ft.      yds. ft.  in. 
Or,  as  27  :  366  :  :  48  :  216  2  8 
For  48X366=17568  which  —27=650^4/^=216 
yds.  2ft.  8  in.  Ans. 
d.       d.      >    m.     m. 

(48)  As  50  :   100  :  :   14  :  28 

For  14X100=1400  which  -f-50=28 men.  Ans. 

PROMISCUOUS  EXAMPLES. 

Cwt.  Cict.  qrs.  lbs.        ^  ds. 

(49)  As  1   :   18     3     19  ::   11  371 

Cict.  qrs.  lbs.     lbs. 
For  18     3     19=2119  which  X  1137i=24l0362Jlthe 
divisor;    which    —1  ctc^.,  that  i3"'ll2  ;6^.=|215 
21-5^  ds.  Ans. 

^      $■      $ 

(50)  730—22=708 

yds.    yd.       $       $ds.m. 
Then  as  156  :   1  :  :  708  :  4  53  8-f-  Ans. 

For  708X  1=708  which  ~-156=g4  53  ds.  8  m.-f  72 


GO  Sl.^GtK  RULE  or  THREE. 

(51)  To  find  the  prime  cost. 

C,     C.   qrs.  lbs.      ^  ttx.         ^    cts.m.. 
1   :   19     2     17  :  :   9  31}   :   183  00  7-f-     ' 
lbs.       lbs.         ^  els.         ^    cts.  m. 
Or,  as  112  :  2201   :  :   9  31|  :   1B3  00  7+ 
For    93lAx2201=:20496Gl|     which    -M12=gl83 

00  cts.  7  m.  4-   Alls. 
To  find  the  sum  it  sold  for. 

lbs.       lbs.  g  cts.       %    cls.m. 

As  112  ;   2201   :  :    10  65   :   209  29   1+ 
For  1065X2201=2344065  which  ~112~: 

C^*.  1  m.  Ans. 
To  find  the  gain.     It  sold  for  ^209  29  cts.  1  »i.— 
Jl83  00  cts.  7  m.rz:g26  28  cts.  4  m. 

yds.   yd.       ^  cts.    cts.m. 

(52)  As  47  :   1   :  :   14  75  :  31  3-f 
For  1475  X  1=1475  which  -^47=31  cts.  3  m.+  Ans. 

(53)  3  qrs.  wide  :  1|  wide  :  :  3 J  long  :  61  long. 

For  3|=15  ^r*.  and  ^\^=:b  qrs.  therefore  15X5= 
75  which  —3=25  ^rA'.=the  quantity  of  hoUand 
requisite  for  each  suit,  and  this  ib  qrs.x'^^^ 
suits  or  men=8850  qrs.  which  —4=22121  yds, 
Ans. 

(54)  First  ^Sft.  :  250  ft.  :  :   33^1;.  10  m.   :  338/?.  4  in. 
For  33  10X12=406  in. X250=101500  which  -f-2c 

=4060m.=338/if.  4in.  the  length  of  the  shadow 
of  the  tower.  Then  as  the  shadow  is  1  Sft.  6  in. 
longer  than  the  width  of  the  river,  consequently 
338/1?.  4  m.— 18/if.  6  m.=319^.  10  in.  the  width 
of  the  river.  Ans. 

(55)  First,  24  hrs,  :   1  m.  :  :  360  deg.  :17  m.  2  fur.  1st 

Ans. 
For  360X691X1=25020  and  24  Ar5.x60=1440; 

therefore  25020-f-1440=17  m.  3 fur. 
Again,  24  hrs.  :   1  m.  ;  :  360  deg.  :11m.  4/ttr.= 

the  velocity  of  the  earth  in  lat.  40  deg. 
For  360X46=16560-M 440=11  m.  4 fur. 
Then,  1 7  m.  3/i^r.— 1 1  m.  4/wr.=5  m.  Ifur.  2d  Ans. 


DOUBLE  JlVhE  OF  THRKE.  (j9 

DOUBLE  UUI.R  OF  THREE. 

EXAMI'J.ES. 

(2)  Thus  3^.  •  ^8  ^..  )  ^^^^^  ^  l70A,2R.2GP,20yd8.+ 

For  8X24X32=61 14  the  dividend. 

And  3  X  1 2=36  the  divisor. 

Then  6144-7-36=170.3.  2  R,  26  P.  207jds,-\-  Ans. 

(3)  Thus  lOox.  :  20ox,  >        ^  /,        ^  ^ 
^  ^  18./.     .27.7.    r'  '      ' 

For  20X27X2=1080  the  dividend. 
And  18X10=180  the  divisor. 
Then  1080-7-180=6  .'I.  Ans. 

W^^^^%^;^-]::   36/6..   :   48 /&.. 

.  For  24X5X36=4320  the  dividend. 
'  And  9  X  10=90  the  divirior. 
Then  4320-r90=48  lbs.  Ans. 

(5)  Thus  $100       :   SJS335      ?  .  .  ^g  .  ^30   15,^, 

For  33r>  X  18  X  6=361 80  the  dividend. 
And  100  X  12=1200  the  divisor. 
Then  36 180-M  200=^30  15  ds.  Anc. 

(6)  Thus  20m.  •  46m.K.  ^.^  3^,^^^^  ^  g^^g  g,  ^^^^ 

For  46X32X5631]=8289200  the  dividend. 
•     And  20X5:;=  100  the  diviBur. 

Then  8289200^  100=g828  92  cf*.  Ans. 

(7)  Thus  n-m.  :   12?7i.  >        ...^       .  r.A    '  • 

30./.   :  90ri.  l'-''   ^^20prm'..:  540;>air.. 

For  12X90X120=129600  the  dividend. 

And  8  X  30=240  the  divisor. 

Then  1 29600—240=540  paiW.  Ang. 

(8)  Thus  12p.  :  38/>.  )        ^^„  ..^  „      ,-0 

4//.   :   16r/.  \  '  *  ^^^^^^-  '  '^^^ ^^''  ^^^''''' 
For  38X16X37=22406  the  dividend. 
And  1 2  X  4=48  t lie  divisor.* 
Then  22496-MJ;r^-.  168  lbs,  lOJor.  Ans. 


70  DOUBLE  RULE  OP  THREE. 

(9)  Thus8/fc.    :   12/i.  >        .'    .         to  Wo  _l 

For  12x7x5—420  the  dividend. 
And  8  X  4—32  the  divisor. 
Then  420-^32=134-  Ans.# 

(10)  Thus  liyds,  :  247jds,2qrs.  >  :  :  gl7  37-J  c^.  :  ,^132 

3qrs.     :     Iqrs,  \  43  d*.-f 

For  24i/ds.  2qrs.=9Sqrs.     And  '7^yds,=30qrs, 
Then  98X7X17371==  11 91 925  the  dividend. 
And  30X  3=9p  the'^divJBor. 
Then  1191925-^-90=gl32  4Scts,+s  Ans. 

(11)  Thus  20^.  :  62h.  )  :  :   Ubu,  :  605w.   3pe.  S^^^.  1;?^ 

22 J.  :  3Gc/.  5  +86 

For  62  X  38  X  12=26784  the  dividend. 
And  20  X  22=440  the  divisor. 
Then  26784-t-440=606w.  3pe.  2qts,  IpL+^iie  Alls. 

For  563X  18X6=182412  the  dividend. 
And  lOOx  12=1200  the  divisor. 
.      Then  182412-^  1200=1^152  Olct     Ans. 

(13)  Thus  8/..    :  -20/..  )  ,  ^  ^^^  ,  ^^^^  ^^^^^^  3^^^^ 

7m.  :   17771.  ^  ^ 

For  20  X  17X6=2040  the  dividend. 
And  8  X  7=56  the  divisor. 
Then  2040~5G=3GT'.  QcwL  2qrs.  Sibs,  Ans. 

(14)  Thus2y./..  :  50t/r/..  )     .^^j^  .   ^^,^^ 

[yqrs.    :      3qrs.  ^ 
For  50X3X  1=150  the  dividend. 
And  2  X  5=10  the  divisor. 
Then  150-:- 10=  15/6*.  Ans. 

For  9QX 3X7=20 16^ the  dividend. 
And  21  X  32=672  th(*  divisor. 
Then  2016-^672=3.  Ans. 


DOUBLE  liULE  OF  THREE.  7  1 

(16)Thu^4m.:     Um.K,^    giOO  :  §360 

For  1 2  X  9  X  100=10800  the  dividend. 
And  4x7-^=30  the  divisor. 
Then  10800~30=$|60.  Aiis. 

(17)  Inversely  thus  40ft. )  :  J  20ft,  ) 

54ft.  5  :  I  i^4ft,  > :  :  lOd.  :  Id,  lO^krs. 

127)1.     :     21m.  ) 
For  20X54X27X  i  0=29 1600  the  dividend. 
And  40  X  54  X  72=155520  the  divisor.  ^ 
Then  29 1600^1 55520= Ic?.  10 J/tr5.  Ans. 

(18)  Thus  305^.^    :   lOj^^^l' j::  sp^  ..   ll6J.-f254Q 

For  1 056  x"  14X30=443520  the  dividend. 
And  305  X  121=38121  the  divisor. 
Then443520^3812l=116cZ.  Ans. 

(19)  Thus  $210       :  g837      )        ^.      07       or      ^r   r 

15w.  :         4m.  5 
For  24w.   ^d.=llld.     And   837X4X171=572500 

the  dividend. 
And  210X  15=3150  the  divisor. 
Then  572508-h.31 50=1 81(i.=25wj.  6c?. +2358  Ans. 

For  5X30X50=7500  the  dividend. 
And  2ix  15— 371  the  divisor. 
Then  7500—37^=^200.  Ans. 

(21)  Thus  5m.  :  34m.  J  .  ,  g^^  ^^  ^^^^  ,  ^3^3^  ^^  ^^^^ 

For  34X90X2050=6273000  the  dividend. 

And  5  X  4=20  the  divisor. 

Then  6273000-^20=^3136  50  ds.  Ans. 

(22)  Thus  24a..:  ^760..  J  ^,  ^,3  .  gj^g  , ,,,,.+  , ,o 

For  76X121X18=165528  the  dividend. 

And  24X45=1080  the  divisor. 

Then  165528^1080=^153  26  cf^.  Ans.+ 


72  DOUBLE  hULE  br  THREK. 

(23)  Thu.42.a,  :  392^^^^^ 

For  392X7X6=10464  the  dividend. 
And  42X  14=:=588  the  divisor. 
Therefore  16464— 588=28^72.     Ans. 

(24)  Thu«  S^cut.  :   ^t.K,p,,as.:$m-!lilcU.i 

For  r>Ox  150  X  050=7126000  the  dividend. 

And  35X20=700  the  divisor. 

Then  7125000-^700=^101  78 J ds.-f     Ans. 

(25)  Thusgll   15ch.  :   ^31      UVids.  }  ::  gl25:g60356; 

97n.  :       lyr.  6mo.   ^  d^'.-f 

For  3118j=12475(/r*.X  18m.  X  125=28068750   the 

dividend. 
And  $11  75d^.=4700^r*.X  9=42300  the  divisor. 
Then  28008750-f-42300=g663  56jds.-f     Ans. 

(26)  Thus  glOO      :  g275      }  .  .  hj..  .   ^7, 

12m.  :        56m.  ^  '  '   »^  '   fc^^ 
For  275X56X6=92400  the  dividend. 
And  lOOx  12=1200  the  divisor. 
Then  92400-r  1200=^77.     An^. 

(27)Thu8g56        :P       ),,p,0:POO 

For  6  X 20 X  560=67200  the  dividend. 
And  56X12=672  the  divisor. 
Then  67200-^-672=^100.     Anjb'. 

(28)  Thus  12yds.  :  75y^..  ),  .^^^  .   ^3^^,^  ^.^^^^ 
59)'*.    :     3qrs.  \ 
For  75X3X5=1125  the  dividend. 
And  12  X  5=60  the  divisor. 
Then  1125-r60=18/6.  12or.     Ans. 


PRACTICE. 


PRACTICE. 


EXAMPLES. 


(3) 


!at?- 


148 

74 


CASE  1. 

(4)    |I|l|3268atl 

Ans.  ^16  34  cts. 


Ans.  $2  22  cts. 


(^) 


4260  at  J 

2130 
1065 


Ans.  g31  95  d^. 


(7)    |2l||634  at  2  miZ/5. 


Ans.  $1  26  8 


(6) 


111115324  at  1 


Ans.  $13  31  cts. 


73 


(5) 


352  at  4  mills, 

70  4 
70  4 


Ans.     gl  40  8 


(9)    |5m3456  at  5  miZZ5.  (10) 


Ans.  $17  28 


498  at  6  mills, 

249 
49  8 


Ans.  $2  98  8 


74 


(11) 


I'KACTICE. 


8462  at  8  mills. 

4231 
1692  4 
846  2 


(12) 


1264  at  7  milk, 

632 
252  8 


Ans.  ^67  69  6 


(13) 


Ans.  $n  84  8 


4628  at  9  mills. 

2314 
923  6 
925  6 


Ans.     $41  65  2 


CASE  2. 

cf5.  d$. 

(2)    |6|| iVi3648  at  6J  d*.      (3)    llO|yVp42  at  10  ds. 


Ans.  $228 


Ans.  $74  20 


cf*. 


d5. 


(4)    |20m8264  at  20  ds. 
Ans.  $1652  80 

ds. 

(6)    |50|1|5876  at  50  ds.        (7) 

Ans.  $2938 


386  at  25  ds. 


(5)     |25p 

Ans.  $96  50 


ds. 
25 

20 


3542  at  i:.  c.'.. 

885  50 
708  40 


Ans.   $1593  90 


(8) 


i'KACTICE. 


ds. 
50 

25 
5 


r31925  at  80  c/5. 


15962  50 
7981  25 
1596  25 


Ans.  ^25540  00 


ci8. 


(9)  |12im4264at  121  d*. 
Ans.  g533 


(10) 


cts, 
50 


dL 


^\   18626  at55d*.  (11) 


9313 
931  30 


Ans.  ^10244  30 


(12) 


cts, 
10 


528  at  16  els, 

52  80 

26  40 

5  28 


Ans.  ^84  48 


(13) 


25 

J  1724  at  371  cts, 

1  431 
215  50 

Ans. 

g646  50 

cts, 
50  j 

^¥8 

13854  at  56  J  ds. 

6927 
865  87  5 

Lns. 

^7792  87  5 

4858  at  29  cts. 


Ans.  gl408  82 


(15) 


cts, 
50 


2267  at  85  els. 

1133  50 

666  75 
226  70 


Ans.  gl926  95 


76 


PRACTICE. 


(16)  |20J»|190at20cf5. 
Ans.  g38 


(17) 


cts, 
6 


3654  at  18f  c<#. 

456  75 
228  37  5 


Ans.  $685  12  5 


cts. 


(18)   50  117638  at  70  c«5. 


8819 
1763  80 
1763  80 


Ans.  gl2346  60 


(2) 


$  cts, 

10  25 

10 


102  50 
5  12  5 
0  64  0 


Ane.  gl03  26  5 


CASE  3. 


(3) 


cts. 


4 

15 
7 

29 

05 

2 

07  5 

1 

03 

7 

0 

51 

8 

0 

14  8 

0 

3 

7 

Ans.  $32  86  5 


PRACTICE. 


77 


Cwt.  qr.  lb,     ^  cts, 
(4)  129  1  10  at  1  05 
129 


(6) 


Ans.  gl35  80  4 

Cwt.  qr,      $ 

130  1  at  15 

130 


450 

15 

1950 
3  75 


Ans.  gl953  75 


qrs,  lb,         cts, 
(8)  2   14  at  2710 


(5) 


Cwt.qr,     g  cts, 

16  2  at  5  18 

16 


3108 
518 


82  88 
2  59 


Ans.  g85  47 


Cwt,  qr,  lb,      cts. 


(7)   25  1 


9  at  175 

25 


ll 

I-    875 

4. 

[350 

4, 

-43  75 

43  7 

I: 

6  2-f 

6  2+ 

1  5+ 

Ans.  $44,  32  8 


(9) 


lb,  oz.  dwt,  gr, 
6  5  10  5  at 


1355 
338  7 


Ans.  gl6  93  7 


g  cts, 
4  16 
6 

2496 

138  6 

34  6 

17  3 

3 


Ans.  g26  86  8 


G2 


78 

PRACTICE 

Ih.  oz.  dwi.gr,     cis. 

.      lh,oz. 

dwt.scr,       cts. 

(10)  27  10  4  18  at  2635       (11) 

9  11  17  22  at  613 

27 

9 

6 

^ 18445 
^  5270 

4^5517 
1  ^    306  5 

10 
5 

2\ 

-    204  3 
51  0 

3 

i711   45 

1 

1    13  17  5 

:      25  6 

4 

]r      6  58  7 

12  J      12  7 

12 

\      2  19  5 

6^        5  1 

6 

V          43  9 
-             5  4 

2|        12 
2^            6 

. 

2  7 

2 

2 

Ans.  g733  92  7 

Ans.  }ei  24  -3 

oz. 

dwL  gr,     cts. 

yd,  qr.      $cts. 

(12)     816 

13    12  at  12^         (13) 

27     3  at  9  65 

1     1 

816 

1 

27 

10 

i  1632 
816 
408 

2J 

6756 
1930 

260  65 
4  82  6 

102  00 

U 

2 

\            6  2 

2  41  2 

j 

\\           12 

J                6 

3 

II 

12 

Ans. 

J267  78  7 

A 

ns. 

gl02  08  3 

= 

PRACTICE. 


79 


yd,    qr,      cts, 

(14)  860  1  at  84 

860 


(16) 


5040 
672 


722  40 
21 


Ans.  $122  61 


gal,    qt,  cts 

428  3  at  140 

428 


1120 

280 
560 


599  20 
70 
35 


Ans.  $600  25 


(15) 


yd.  qr,  na,       cts, 

126  2  2  at  475 

126 


2850 
950 
475 


598  50 
2  37  5 
59  3 


Ans.  5^601  46  8 


gcU,  qt.  pt,        cts. 
(17)   765  3  1  at  21 8 J 

4 


875 

765 


4375 
5250 
6125 


6693  75 
4  37 
2  18 
1  09 


4)6701  39 
Ans.  $1675  34J 


80 

hhd,  g'al. 
(18)   5 


PKACTICE. 


$  Qts, 


31|  at  47  12 


3H 

^ 

5 

233  60 
23  56 

AnB.  g259  16 

hhd,  gaL  qt.       ^  ds, 

(19)   17  15  3  at  64  75 

17 


(20) 


bu,  pe,     cts. 
120  2  at  35 
120 


700 
35 


Ans. 


4200 
17  5 

42  17  5 


hu.  pe.qt.pt.      cts, 
(22)  1354  1  5  1  at  25 
1354 


100 
125 

75 
25 


338  60 

6  2.1 
3U 


3i^ 


Ans.  ^338  60  5} 


453  25 
647  5 


1100  75 
9  25 
3  08  3 
3  08  3 

77  1 


(21) 


Ans.  gllie  93  7 
hu,  pe.  qt.        ^  cts. 
780  3  2  at  1  17 

780 


9360 
819 


912  60 
58  5 
29  2 

7  3 


^. 


Ans.  ^913  55  0 
R,   P, 


(23)  35  2  18  at  54  35 
35 


16 


27175 
16305 


1902  25 
27  17  5 
5  43  5 
67  9 


Ans.  gl936  53  9 


PRACTICK. 


81 


A.R,P.       $  cLs, 
(24)  146  3  10  at  35  10 
146 


A.  R.P.      $  ds. 

(25)  750  1  4  at  12  25 

750 


21060 
14040 
3510 


5124  60 
17  65 
8  77  5 
2   19  3-f. 


61250 
8575 


9187  50 
3  06  24 
0  30  6| 


AnB.  $9190  86  8| 


Ans.  $5153  11  8-f 


APPLICATION. 


Cwt.qr.lb,      i  cts, 
(1)  84  2  14  at  10  60 
84 


CwLqr.lb,    cts, 
(2)  17  1  7  at  1212| 
2 


14 


4200 
8400 


882  00 
5  25 
1  31  2-f 


Ans.  $888  66  2-f 


2425  halves. 
17 


16975 

2425 


412  25 
6  06  1^ 
1  51  5| 

2)419  83  8  mills. 


Ans.  $209  91  9  mills. 


82 

T.cwLqr.     $   ds. 

(3)  15  10  3  at  80  15 

15 


PRACTICE. 

yd.  qr,  pie,      yd, 
(4)  35  2X170=6035  at} 
6035 


10 


40075 
8015 


1202  25 
40  07  5 
2  00  3J 
1  00  U 


4)6035  qrs, 
Ans.  p5   08 


Ans.  gl245  33  0| 

A,  R,  P.      $  ds, 

(5)  175  3  12  at  52  15 
175 


26075 
36505 
5215 


9126  25 

26  07  5 

13  03  7 

3  25  9 

0  65  1 


Ans.  $9169  27  2 


(6)  1365  at  ld,=$6   82|c^.  Ans. 


(7)  784  at  84  di. 

784 

336 
672 

588 


Ans.  g658  56 


PRACTICE. 


83 


(4)    [l[j|475at| 
12)118f 


STERLING  MONEY. 
CASE  1. 

(5)    mi[299atj 

12)149| 


Ans.    9*.  lOfdf. 


(6) 


Ans.  $l2s,  5|cf. 

978  at  I 

489 
244^ 


12)7331 
210)6|1  1 


Ans.  £S  Is.  Ud. 


(2)      1241978  at  2d, 

2|0)16|3 

Ans.  £8  3^. 


(4)      [6j||792  at  6d. 

2|0)39|6 

Ans.  £19  16^. 


CASE  2. 
(3) 


499  at  5J. 

166  4 
41  7 


(5) 


2|0)20|7  11 

Ans.  £10  7*.  Ud. 
1 


888  at  9d. 

444 

222 


210)66|6 
Ans.  £33  Ss. 


84 


(6) 


PRACTICE. 

921  at  lid. 


460  6 
230  3 
153  6 


2|0)8414  3 


Ana.  £42  4*.  3d, 


CASE  3. 


(2)      |3|||487  at  15d. 
I  I  |l21  9 

2|0)60I8— 9 

Ans.  £30  8*.  9c?. 


(3) 


979  at  22J 
489  6 
244  9 

81  7 

20  4£- 


2|0)181|5  2J 
Ans.  £90  15*.  2|cf. 


(4) 


532  at  23j<f. 
266 
177  4 
44  4 

22  2  4 

n  1  J 


2|0)105|2  11 J 


Ans.  £52  12*.  ll|<f. 

CASE  4. 
(2)        ,5|||489  at  5«. 


Ans.  £122  5*. 


PKACTICE. 


85! 


(3) 


937  at  11*. 

468  10 
46  17 


Ans.  £515  7*. 


(4) 


1286  at  15*. 

643 
321   10 


Ans.  £964  10*. 


(5) 


2798  at  19*. 

1399 
ft99  10 
559  12 


Ans.  £2658  2*. 


CASE  5. 


(2) 


10 


£  *.  d. 
569  at  4  13  71 
4 

2276 
284  10 
56  18 
28  9 
14  4  6 
2  7  5 
1  3  81 


(3) 


Ans.  £2663  12  7| 


101 

h-J 

\\ 

6- 

3- 

3 

T¥ 

£  *.  df. 
1967  at  5  16  9f 
5 

9835 
983  10 
491  15 
98  7 
49  3  6 
24  11  9 
6  2  \\\ 


Ans.  £11488  10  2|. 


H 


86 

ritACTICE,                                               II 

(4) 

10^ 

1 : 

?  ^ 

^    2975  at  £7 

195.  llj(f.                   1 

20825 
-    1487  10 
743  15 
.      595 

99     3    4 

24  15  10 

12     7  11 

6     3  11 

3     1   11 

Ans. 

£23796   18^  OJ. 

CASE  6.                                      II 

(2) 

C.  qr.  lb. 

9    2     17  a 

.    !      i 

£    5.    ^.         C. 

14     7     6  (3)    11 
9 

1 

/6. 
16  a 

£    ^   rf. 
t5     6     71 
11 

21 

2] 

u 

39     7     6 
2     3     9 

0  10  in 

1     6J 

1 

14 
2 

T 

58  12  101 

1     6     7| 

13     33 

1  io| 

An«.   £42     4     fil                  ^"^-  ^ 

60  14     8-H 

(4) 

7  3  22 
1 

It  1    18  4 
7 

"4 

1    (5)27     1    19 

1 

at' 

r 

7 

1 

! 

2  17  8> 

3X9=27 

2' 
1^ 
14  J 
7) 
1  ^ 

-13     8  9 

0  19  2 

9  7 

49 

24 

4 

t 

1 

14 

4 
1 

8  13  0| 
9 

7  17  6J 

14  5-f 

7  21 

£»     1 

Ans.  . 

ei5     5  0 

i                Ans. 

£79     1  8?              1 

1 

TARE  AjN'D  tret.  87 

TARE  AND  TRET. 

CASE  1. 

CwL  qr,  lb,  Cwt.  qr.  lb.  Cwt.  qr.  lb. 

(2)    7     3     20  (3)    6     2     5  (4)     369     2     21 

8  «—     1   11  —10     1     12 


gross  63     1    20        Ans.  6    0  22        Ans.  359     1 
—5     1     19 


Ans.  58     0 


CwLqr.lb.  C.qr.lb.          lb. 

(5)        6  1  19^  (6)  No.  1.3  2  19  tare  34 

8  No.  2.  6  0  13  tare  57 

No.  3.  4  3     5  tare  46 

43  1  12  whole  gross.      — C.qr.lb. 

—2  0  23  tare.  14  2     9w.t.l37==l  0  25 

—1  0  25 

Ans.  41  0  17  neat. 


Ans.  13  1  12 


CASE  2.' 

C.  qr.   lb.  qr.  lbs. 

(2)      4     2     24  2     18 

7  7 


33    0      0  gross.     4cwt.  2qrs.  14^6*.  whole  tare. 
4     2     14  tare.      ^    


Ans.  28     1     14  neat. 


TARE  AND  TRET. 


(3) 

C. 

21 
3 

qr.    11 
2     2 
0     1 

\ 

J  at  5  50 

Neat  18    2      t 

-^ 

% 

*. 

i 

4400 
550 

lb 

1 

1 

2 

9900 
275 
9  8+ 
4  9 

Ans 

.  glOl  89  7 

(4)          2 

qr.  Ib.^ 
1     25 
9 

lb. 

30 

9 

C.  9r.  lb 

ross.              270=2    1    18 
re. 

$cts. 

t  5  10 

19 

22 
2 

1       Ig] 
1     18  ta 

Neat  19 

3     11   a 

qrs. 

^   i 

4    ? 

45  i 
51  ( 

)0 

) 

)0 
)5 
11  5 

M   8+ 

8  2-f- 

96  i 
2  £ 
1  S 

1 

Ans.  $ 

101  22  5  value. 

TARE  A3SD  TRET 


89 


CASE  3. 

C.  qr.   lb. 
(2)  7     3     14 

4 
lbs 


31     2       0  gross. 


4    2       0 
1     0     14 


5    2     14  tare. 


Ans.  25    3    14  neat. 


C.  qr,  lb, 

(3)  5     1     13 

10 

lbs. 


16 


53    2     18  gross. 


7    2     18+  tare. 


Neat  46     0      0  at  8  75 
46 

5250 
3500 


Ans.  ^402  50  value. 


H,^ 


'90 


TARE  AND  TRET. 
(4)  4C.  Iqr,  24/6. 


26     3      4  gross. 


Tare    4     l 


Neat  22    1 


8+ 
25+ 


Ibi. 


27=2519  at  74 

—   7j        - 

17633^ 
1259  5 


Ans.  $188  92  5  value. 


CASE  4. 
(2)  2C.  Xqt,  lOlb, 

12 

lbs. 

28     0       8  gross. 


4    2       1  tare. 


7  suttle. 
17  tret. 


Neat  22    2     18   at  19  60 

— —  22 


lbs. 
14 

2 
2 


39  20 

392  0 

431  20 

9  80 

2  45 

35 

35 

Ans.  g444  15  value. 


(3) 


I"'  '  = 

TARE  AND  TRET. 
C.  qr,    lb, 
4     1     11 
6 


91 


gr,  lb, 
1     5 
6 


iie     0     10  ^ 
13      2  tare. 


cwt,  13    2  tare. 


^)24     1       8  suttle. 
"^  — 0     3     20  tret. 

$  ds. 

Neat  23     1-    16   at  6  75 

^  23 


qrs. 
1 


20  25 

135 

0 

155 

25 

1 

68J 
84;- 
12 

Ans.  gl57  90  value. 


APPLICATION. 

C,  qr,  lb, 
(1)  17     3     22  gross. 

3     14  tare. 
'  —      lbs,        ds. 

Neat  17    0      8=1912  at  23". 


5736 

3824 
478 


Ans.  g444  54 


92 
(3) 

(2) 

5C 

r 

8" 
K 

Neat  7 

C.qr. 

6  3 

7  0 
5     3 

8  0 

TARE  AND  TRET. 

\  2qr.  19Z6. 

3X5=15 

i 

2qr.  25/6. 
3 

No.  1. 

No,  2. 
No.  3. 
No.  4. 

7     0 

1                         2 
5 

0     19 
5 

3     0       5gl 
3     3     11  ta 

•OSS.      C.IO 

3    11  tare. 

t  g6  75d^. 

74 

le. 

4     0     22  a 

16^ 

2- 

-    27  00 

472  5 

499  "50 

r          96 

z          24 

12 

/6. 
18 
10 
26 
3 

A 

grog 

tare 
atj 

ns. 

g500  82  vail 

8 
4 

tV 

i 

28 

0 

1 

s» 

^3  75c<^. 

2 
1 

0 
0 

0 
0 

Neat 

3 

0 

0 

25 

0 

1 

lb. 
1 

rh 

3  3 

18  ' 
75  ( 

93  ' 

Ai 

IS.  ^ 

93  78  3  value. 

(4) 


TARE  AND  TRET. 

IC.  tqr,  23lb. 

4X6=24 


93 


5     3 


34     3     20  gross. 
3    3     12  tare. 


18^6. 

24 

72 

^    C.qrAb, 
432=3  3  12  tare. 


Neat  31    0      8  at  $5  l'7^cls. 
2 


1035  halves. 
31 


1035 
3105 

32085 
73  9 

2)32168  9 


Ans. 


79  4  value. 


(5) 


IC.  l^r.  13Z&. 

3X5=15 


4     0 


11 

5 


20     1     27  gross. 
2     3     22  tare. 


22/6. 
15 

110 

J!«.  C.qrJb. 
320=2  3  22  tare. 


Neat  17    2 


5  at  $9  64ctg. 
—  17 


2 

1 

2 

67  48 

lb. 

96  4 

163  88 

4 

A 

4  82 

1 

5^ 

34  4 
8  6 

Ans.  g 

,169   13  0 

94  inte:^est. 

a  qr,  lb. 

(6)  6     2     14 

10 

lbs. 

66     1       0  gross. 


9     1     24 
1     0    20 


10    2    16  tare. 


55    2    12  suttle. 
2    0     16  tret. 
lbs. 


cts. 


Neat  53     1     25=5989  at  lU 


"i 


65879 
2994  5 


Ans.  ^688  73  5  value. 


-MtoQeiM 


INTEREST. 


EXAMPLES  IN  CASE  1. 


(2)         225 
7 


$    cts, 

(3)         384  50 

5 


Ans.  5515  75 


Ans.  gl9  22  5  m. 


INTEREST.  9& 

£      8,  %     cts. 

(4)     580  10  (5)     1654  81 

6  5 

r-            J6    *.  eif. %cts. 

£34  83  0  Ans.34  16  7  g82  74  05     Ans.  82  74 

20  


5.16  60 
12 
rf.7  20 


^  j6         £  s.  d» 

(6)    IllillSOO         (7)  350   ^Ans.  18  7  6 


Ans.  $1  50 


1750 
87  10 

£18  37  10 
20 

^.7  50 
12 

d,e   00 


(8)          |J|524  (9)         111842 

2620  4210 

131  421 

Ans.  g27  51  Ans.  g46  31 


96                                           XNTEKEST. 

CASE  2. 

$                 £    s.d,      £  8,  d. 
(2)    540         (3)  124  5  6        4  19  5  Int  for  1  year. 
5                           4                  3 

27|00           £4197  2  0    £14  18  3  Ans. 

Ans.  g54|00           «.19|42 
12 

rf.5|04                                                                    ; 

(4)              482 
6 

g28f92  interest  for  1  year. 
7 

Ans. 

g202|44 

CASE  3- 

(2)          325 
4 

mo. 
2    , 

^  13|00  Int.  for  1  yr. 

4                                                                    ; 

i 

52      Int.  for  4  yrs. 
2|16|6  Int.  for  2  mo. 

Ans.  $54  16  6                                                         1 

INTEEE8T. 


97 


(3) 


840 
4 


33160  Inti  for  1  yr. 
6 


168 
8 


00  Int.  for  5  yr. 
40  Int.  for  3  mo. 


Ans.  gl76  40 


(4) 

mo. 

4 


840 
7 


58|80  Int.  for  1  yr. 
5 


294|00  Int.  for  5  yrs. 
19|60  Int.  for  4  mo. 


Ans.  $313  60 


(6) 


1200 
5 


Ans.  g60  00  Int.  for  1  yr.  Then  say,  nslyr.:  15w. 

^  $^^  '•  $^'^  30c<5.  Ans. 

(7) 


240 


960 

120 

60 


Ans.  gn  40  Int.  for  1  yr.  Then  say,  as  lyr.  :  61d. 
gll  40:  gl  90cfe.  Ans. 


98  INTEREST. 

£ 

(8)      1000 
7 


£70  00  Int.  for  1  yr.    Then  as  lyr. :  Umo.  : :  je70  : 
£81  13*.  Ad     Ans. 


(9)      450 
51 


2250 

225 


$U  75  Int.  for  1  yr.     Then  as  \yr.  :  6mo.  20d.   : ; 
g24  ISds.  :  $13 15cts.+  Ans. 

$    cts. 
(10)      375  25 
6 


^22  51  50  Int.  for  1  yr.  Then  as  lyr. :  Syrs.  2mo,  2w, 
5rf.  : :  g22  Bids.  5m,  :  $72  85.  Ans. 


CASE  4. 


(2)  854 

30 


6)25620 
Ans.  ^4  27  0 


(3) 

$ 
1100 
48 

8800 
4400 

6)52800 

Ans. 

$S   80  0 

INTEREST. 



09; 

$ 

(4)          3459 
75 

$ 
(5)           1500 

60 

17295 
24213 

6)90000 

jl  111  15000171.  at 
—2500 

1 
6  per  cent. 

6)259425 
Ans.  g43  23  7 

Ans.  gl2  50  0 

CASE  5. 

(2)         6  yrs. 
4  dolls. 

24  Int.  of  jSlOO  for  6  yrs. 
-flOO 

£124  amount  of  £100  for  6  yrs. 

Then  as  £124  ;  £1240  : :  £100  :  1000. 
(3)          6  yrs. 
6  dolls. 

Ans. 

30  Int.  of  glOO  for  5  yrs. 
100 

gl30  amount  of  glOO  for  5  yrs. 

Thenasgl30 

:  $2470::  $100:  $1900. 

Alls. 

(2) 

CASE  6. 

$ 
1476  amt. 
1200  prin. 

$276  Int. 

And  gl200  :  $100  :  ; 

time. 
Then  as  byrs.  9mo,  : 

$276  :  $23  int.  of  $100  for  the  i 
$23  : :  lyr.  :  $4  per  cent.  Ans. 

same 

100  INTEREST. 

$    cts. 
(3)  927  82^  amt. 

834  00"  prin. 

^93  8;21  int. 

As  g834  :  §93  ^^cts777pQ^Q  :  gll  2octs. 
And  then,  as  2yr*.  6mo.  :  §11  2bcts,  : :  iyr, :  §4|  per  cent. 
Ans. 

CASE  7. 
£  £ 

(2)  1600  2048 

4  1600 


£64  00  :  Iyr.  : :  448  :  tyrs.     Ans. 


(3)      1000 
41 


40  00 
5  00 


§45  00  :  Iyr.  : :  §281  25ctjf.  :  6yri,  3f»o.     Ans. 

COMPOUND  INTEREST. 

§ 

(2)      760  prin.  * 

6  rate  per  cent. 

45  60  int.  1st  year. 

805  60  amt.  of  let  yr.  and  prin.  for  the  2d  yr. 
48  33  6  int.  of  2d  yr. 

853  93  6  amt.  of  2d  yr.  and  prin.  for  the  3d  yr. 
51  23  6  int.  of  3d  yr. 

905  17  2  amt.  of  3d  yi;. 
760  00  0  1st  prin. 

Ans.  §145  17  2  compound  int. 


INTEREST. 

£,    s.  d,             £     8.    d. 

(3)      242  10  6             242  10     6 

6              14  11     Oint.  Istyr. 

lOll 

£14|55  3  0             257     1     6  amt. 

20                    15     8    5|  int.  2d  yr. 

11|03                  272     9  ll|amt. 
16     7    0    int.  3d  yr. 

288  16  1  If  amt. 
17     6     7i  int.  4th  yr- 

306     3     7  amt. 
^242  10    6  1st.  prin. 

Ans.  63  13     1-f  com.  int. 

(4)      1300 
5 

•65|00  int.  1st  yr. 
1300 

1365  amt. 
5 

68|25  int.  for  2d  yr. 
1365 

1433|25  amt. 
5 

71  66|2  int.  for  3d  yr. 
1433  25 

Ans.  gl504  91  2m.  amt. 

-  u—     ■— 

102 

$ 
(5)      3127 

INTEREST. 

t 

3127 
140  71  5  int.  of , the  1st  yr 

12308 
1563  5 

3267  71  5  amt. 
147     4  7  int.  2(1  yr. 

gl40  71   5 

3414  76  2  amt. 
153  66  4  int.  3d  yr. 

1»R( 

$    Cts. 
(1)          620  25 

3568  42  6  amt. 
160  57  9  int.  4th  yr. 

Ans.  g3729  00  5  amt. 

JMISCU0U8  EXAMPLES. 

(2)      420 
7 

3101  25 
310  12 

£29  40 
20 

nt.  for  1  Jrr.         *.8  00    Ans.  je29  8* 

$ 
1450 

60 

34  11  37 i 
5 

Ans.  gl70  5B  ^m 

(3) 

6)87000 
14500  mills=gl4  hOds.     Ans. 

INTEREST. 

103 

£     s. 
(4)          626     5 

3131     5 
156  11  3 

£     s. 

626     5 

32  17 

d, 
0 
6Jint.  of  the  Istyr. 

659     2 
34  12 

6|  amt. 

1    int.  of  2d  yr. 

£32187  16  3 
20 

693  14 
36    -8 

7f  amt. 

5    int.  of  3d  yr. 

«.17|56 
12 

rf.6|75 
4 

Ans 

730     3 
—626     5 

OJ  amt. 
0    prin. 

.  £103  18 

0|+  compound  mt. 

fr*.3|00 

£ 
(5)          1659 
4 

r£66|36 
20 

Int  for  1 

yr.. 

«.7|2e 
12 

£^.2|40 
4 

5r.l|60 

Then  as  365  days : 
Ans. 

21  days : :  £66  7^.  S^rf.  :  £3 16*.  4j(f.+ 

104 


INSURANCE,  COMMISSION  AND  BROKAGE. 


(6) 


500 
8 


840  00  int.  for  1  yr. 


Then  as  g40  :  gSOO  :  :  lyr.  :  12yrs,  6mo.     Ans. 

(7)  Thus,  Qyrs.  and  6mo.  at  2  per  cent. =^13  interest 
on  glOO. 
Then  ^13+gl00=:gll3=amount  of  glOO.    ^ 
And  as  gll3  :  p50  :  :  glOO  :  g221  22ct8.  9m.     Anfl. 
£ 
(8)        450  amount. 
300  principal. 

£150  interest. 

Then  as  £300  :  £100  : :  £150  :  £50  which  divided  hy 
the  5  years=10  per  cent.    Ans. 

INSURANCE,  COMMISSION  AND 
BROKAGE. 


EXAMPLES. 


£ 

(2)      1320 
5 

Ans.  £66|00 


(3)      3450 
41. 


m 


13800 
1725 


$ 
1680 


n 


3360 
840 
420 


Ans.   $l55\25cts.  

g46|20  commifl  . 

gl680— g46  20cfe.3=gl633[80cf5.    Ans. 


£ 
(5)      7G0 


INSURANCE,  COMMISSION  AND  BROKAGK. 

$ 
(6)   i  ^    5630 

n 


4560 
380 


£49140  Axis.  £49  8*. 
20  

«.8|00 


39410 
2815 
1407  5 


Ans.  g436|32|5m. 


105' 


17654 
181 


141232 
17654 
8827 
4413 


Ans.  g3310|12. 


(8)      2150 
Ana.  £43100 


$     cU, 
(9)  J  |||984  50 


984  50 
246  121 


Ans.  gl2|30|62l 


(10)  i  iJllSsO  75 

"  U li 

1650  75 
825  37! 


Ans.  g24|76|12i 


106 

DISCOUNT. 

DISCOUNT. 

EXAMPLES. 

(2) 

Thus,  2mo. 

at  6  per  cent. 

per  an.=±gU  int.  of  glOO 
+  100"' 

1011  amt  of  do. 

•■ 

Then  as  glOlJ  :  g850  : 

Ans. 

:  glOO  :  g837  43cts.  8w.+ 

(3) 

Thus,  9r/io. 

at  6  per  cent. 

per  an.=g4i  int.  of  g  100 
100 

1041  amt.  of  100 

Then  as  ^ 
present 

,1041  :  g645 
worth. 

::  glOO  :  ^61 7  22cts.   4m. 
645  00  0 

Ans.  $21  11  6 

(4) 

Yrs, 
4 
5 

20  int.  of 
100 

glOO  for  4  yrs. 

gl20  amt.  of  do. 

en  as  ^120 

$115  SOds. 

:  glOO  :  ^646  25ct8,  Ans. 

J/ 

Sino.  at  6  per  cent,  per  an.=^4  int.  of  ^100 
100 

gl04  amt.  of  do. 

Then  gl04  :  ^580  : :  g 

100  :  $551  69f^*.-f-     Ans. 

DISCOUNT. 

107 

Yrs. 
12 

ii 

131  int.  of  100 
100"' 

gllSiamt.  of  do. 
Then  as  gll31  :  g954  :  :  glOO  :  $U0  52cts. 

8m.  Ans. 

(7)     Thus,    15 mo.  =  l^yr,    at    7   per    cent. 
num=g8|  the  discount  of  100. 
100 

per   an- 

glOS^amt. 

Then  gl08|  :   g205 
sent  worth. 

: :  glOO  :  gl88  BOcts, 
205  00 

5m.  pre- 

Ans.  ^16  49  5 

(8) 

mo, 
6 

I 

2 

5 

3 

i 

s 

3f  discount  of  100 
100 

gl033  amt. 

Then  as  gl03f  :  g775  :  :  glOO  :  $146  9Scts. 

7m.  Ans. 

108 


(9) 


mo»   £ 


1 


DISCOUNT. 

mo.    £ 
Again  |  3  |JI6 


H 


15  7710. 

5  dig.  of  lOafor  lOmo.     71  dis.  of  100  for 
100  100 


Jl05  amt. 


1074 


1005 
—475 

Rem.  530 


Then  as  105  :  475  : :  100  :  452  38.    Ans.  to  first  part. 
Again   1071  :  530  :  :  100  :  493  02  4 

Ans.  g945  40  4m, 


(10) 


2260 
6 


Again    6 
5 


135  60  int.  fori  yr. 
5 


678  00  int.  for  5  yrs. 


30  dis.  of  100 
100 

|Jl30  amt. 


Then  gl30  :  te60  : :  glOO  :  gl738  46cts,  Sim.  pres.  wr. 

2260  00  0 

521  63  8  discount. 
678  00  0  interest. 


Ans.  ^156  46  2 


EQUATION.  109 

(12)      782  (13)      476  (14)      1335 

4  3  6 


£31|28             Ans.  $U\2iicts,  33  10  dis. 

20  1335  00 


*»5|60    Ans.  £31  5s.  7J.  Ans.  jJlSOl  90cts, 

12 

d.l\20 


650 
4-* 

2600 
325 


29 1 25  discount. 
650|00 


Ans.  g620|75 

EQUATION. 

EXAMPLES. 

t 

(2)      250X6=1500 
250X8=2000 

500  3500-^500=:7mo.     Ans. 


no 

BARTEK. 

(-3) 

£ 
100x2=200 
100X4=400 
100X6=600 

300        1200-f.300=4mo,    Ans. 

(4) 

100X3=  300 

200X5=1000 

•  250X8=2000 

550          3300-^550=6/na.     Ans. 

-^*^«^- 

BARTER. 

EXA:\irLES. 

(1)  Thus  2c 
Then  as 

wl.  2qrs.  13/6*.=±.?93/6a.  X  0c/*.=:2637c/*. 
25cts,  :  2637c/*.  :  :  1/6.  .  105/6*.  moz,  Ans. 

(2)  Thus  2500/6«.X4^c/5.=^112  50d*. 

Tiien  as  ^1  SOci^.l  ^112  50d*.  :  :  1//^  :  86/6*.  802:.+ 
Ads. 

(3)  Thus  10a/5*.X5?1  25r/.9.=r^t35  OOc^*. 

Then  as  U'icts,  :'gl35   mcU,  :  :  lib,  ;  1542/6.   13o^.+ 
Ans. 

(4)  First,  as  \cwL  :  $3  75<?f^.  :  :  14nc«.  Sqrs,  2Gibg.  :  ^56 
186/*.  3m.  the  value  of  the  rice. 
Then  as  p   Sl^ds.  :  $56  Ucfs.  3m.  :  :   1/6.  :  29/6*. 
150^.+'  Ans." 

(5)  Jims  2cwL  ^qrs,  17/6*. =32 5/6*.  X  12-k/*.=g40  621c/*. 
Then  as  37c/*.  :  ^40  G'Zlds.  :  :   lyd.  :  109yds.  2qrs. 
Ans. 

(6)  Thus  3576t«.  X  0Ms.—p2^  0 1  cL 

Then  4Fycls.  :  g332  Olc/.  :  :  l6tf.  :  7376?/.  3/)«.H-   Ans. 

BARTEK.  1 1  I 

(7)  Thus    UcwL    Oqr.   21lhs.=:n01lhs,X20cls,  =$341 

AOcls. 
Then  ^9  50cts.  :  ^341  AOds,  : :  Icwt  :  35cw/.  2qrs. 
20lbs,-\-     Ans. 

(8)  Th\\s95yds.X5pie.=z4'75yds.x22cts.=$\09  25cts, 
And  32  sheep  X  250=  —80  00 

SR29  25  rem. 


Then  as  gl  50d^.  :  $29  25cts,  :  :  Icwt.  :   19cwt,  2qrg. 
Ans. 
1^9)  Thus    USeyds,   at   43c/^.    per   ijd.  =  $552  9Hcts. 
And  2c«j^.  Iqr.  13lbs.=265lbs.Xl4cts.=z37  10— 


Ans.  $515  88 

(10)  Thus570/&*.X7cA9.=$39  90ds. 

Then  as  ll|c^5.  :  $39  90c/^.  ::  lib.  :  SUIhs,  l5oz.+ 
Ans. 

(11)  Thus  U2cwt,X$5  0\ct8,=:$564  COds. 

Then  as  UOSyds.  :  $564  GOds.  : ; !?/(/.  :  40ds.  7m.+ 
Ans. 

(12)  Tims  750^fe#.xgt  08^^*.— .$810  OOcf^. 

Then  Sr^.v.  ;  $810  OOd*.  :  :   Mb,  :  I0\25lhs.=^90cwt. 
Iqr,  lUbs,     Ans. 

(^S)  Thus2Mr/*.=126^a/5.X75rY,?,~$94  50cU,  ^ 

Then  56yds.  :  $94  5()ds.  ::  1?,'^/.  :  $1  68jc«#.  Ans. 

fi4)  Thus  2108/6*.  XlOd5.=$210  80cf^-. 
And    3ldoz.XU\ds,  ■=  +3  56^ 


$214  361  amt.  of  the  whole. 
—  135  25*^ 


$79  111  rem. 

Then  as  $1  58cf9.  :  $79  \\\ds.  :  :  \hu.  :  50har.+ 
Ans. 


112  LOSS  AND  GAIN. 

(13)  Thus  newt.  X  4X  28=1904/6*.  X  13lcts,=$25'7  04cU. 
value  of  A.'s  g^oods. 
And  1200/?;*.  ot  the  rate  of  gl4  per  cwt.=150  00 

balance  of  B.'s  goods.  

Ans.  A.  is  to  receive  ^107  04 

(16)  Thus  25cts, 
—20 

5  gain  on  20cf*. 

Then  a^  5cts.  :  20cts,  :  :  5cts.  :  20ch.     Ans. 

(17)  Thus  CiOcis,  :  50cis.  ::  31  Jd*.  .  Sorts.     Ans. 

(18)  Thus  105  tons  at  pO  03  per  ton=^1053  IScts. 
value,  of  the  iron.  

pays  cash         650  00 
250/7>s.  at  20cfs.  per  lh.=  50  00 

10  loads  X  156?/.  X  45cc^*.=  67  50 

And  fi5gah.  at  the  rate  of  g75  per  hhd.=lO\   19 

—868  69 
1053  15 


Rem.  unpaid  gl84  46 

Then30d^.  :  ^184  4Cd*.  ::  lib.  :  615Z6*.  nearly. 
Ans. 


LOSS  AND  GAIN. 

EXAMPLES. 

(2)  Thus  lOds. 

—a 

2 
Then  1/6.  :   17G3/6.f.  :  :  2ds.  :  p5  2Gch.     Ans. 


LOSS  AND  GAIN.                                       113 

(3)          Thus  g5  2^cts. 
~5  00 

25  gained  per  barrel. 

Then  Xhar,  :  3636ar.  : :  25cts.  :  $dO  Ibcts.     Ans. 

(4)          Thus  g3  90c^^. 

—3  75 

15  gained  per  yard. 

Then  lye?.  :  \BQyds,  ::  15c^5.  :  g22  50c/*.     Ans. 

(5) 

First,  IcwL  :  g7  SOr/^.  : ;  ISaof.  2^r*.  :  gl38  75d*. 

the  cost. 
Then  U^t,  :  %1  ISds.  :  :  18cw/.  ^rs.  :  ^143  37icf*. 

sold  for.                                                      

Ans.   gained  ^4  62| 

(6) 

First,  210  rcam5X$2  621=^551  25d5.  the  cost. 
And    210ream*x|2  87|=|603  75ds.  sold  for. 

Ans.  g52  50  gained. 

(7)          Thus,  sold  for  $20  Ibds, 
cost     la  12j 

gained  g2  62|  Ans. 

(8)         First,  50cf*. 

—45 

5 

Then  16m.  :  1506w.  :  :  Bcis.  :  p  50cts.     1st  Ans. 
Again,  BOcts,  :  5cts.  : :  glOO  :  glO.     2d  Ans. 

K  2 


114  LOSS  AND  GAi:^. 

(9)  First,  760/6*.  X  90d.9.=g684  00  sold  for. 
810  00  cost. 


Lost  126  00  1st  Ans. 


-J 


ThcngOlO  :  $126  ::  ^100  :  gl5|.     Ans. 
(10)  First,  Slllds. 

Then  31^cts.  :  B^cts.  : :  $100  :  gl4|  per  Cent.     Ans. 

(11)  Thus  15.  :  2(1  :  :  £100  :  £162  per  cent.     Ans. 

(12)  Thusgl3  75d.?.  First  cost  of  each  piece. 

3  12^  for  dyeing. 

gl6  J]7|  whole  cost. 
ThenglOO  :  $112  ::  $16  871d*.  :  $18  90ci*.  Ans. 

(13)  Thus  Iciof.  :  1/6.  ::  $7+$3  :  ^cts.  9m.     Ans. 

(14)  Thus,  paid  22cts,  per  lb. 
Sold  it  for   19 

Lost    4cts.  per  lb. 

Then  as  1/6.  :  702/6*.  :  :  4cts.  :  $28  OMs.     Ans. 

(15)  Thus  S2  23c/*.  :  $2  75c/*.  ::  $110  :  $135  65c/*. 
And    $135   65c/*.— $100=:$35   65c/*.=:35|-  nearly. 

Ans.   ' 

(16)  Thus  $100  :  $125  :  :  $2  lOcU.  :  $2  i62lc/*.  what 

1  hox  sold  for. 
Then  as  $3  50c/*.  price  of  Icwt.  :  $2  62^/*.   price 
of  1  box  ::   112/6*.  :  84/6*.     Ans. 


LOSS  AND  GAIN.  115 

(17)  First,  lOpie.  X  gl4=g224  the  prime  cost. 

And     5pie.X$ll=:$H5 
6pie.X$i5=^pO 

^175  received  back  again. 

Then  as  ^100  :  gll2  : :  g^24  :  ^250  SSds.  price  of 
the  whole  with  rate  per  cent,  added. — 175  00 

5)75  08  price  of  the 

5  pieces. 

Ans.  gl5  17  G  perpze. 


(18)  Thus  ^500—^410=^90  gain  on  the  whole. 

Then  as  31211)8,  :  lib.  :  :  ^a0:24d*.  Iw.-f     Ans. 


19)  Thus  $1  :  glOO  :  :  5cts.  :  $5  00  the  Ans. 


(20)  First,  ^1  05r!.«f.X5l0— ^535  50d*.  prime  cost. 
And    ^1  30ci6\XiA0—^QC)3  OOcts.  sold  for. 


mo, 

3 


6 

1   50 
100  00 


glOl   50 


Then  glOT   BOds.  :  glOO  :  :  ^,663  :  $^353  20cf*.+ 
Hence    $653    20c^«.  — ^535    50r^.  =  ^117    70^5. 
Ans. 


116 


FELLOWSHIP. 


FELLOWSHIP. 

EXAMPLES. 
CASE     I. 

(2)  Thus  D.'s  stock  ^500 

E.'s  400- 

F.'s    ,  300 

Sum  1200 


Then  as  t^OO  :  500  :  :  300 
And  1200  :   400  :  :   300 

And         1200  :  300  :  :  300 
(3)     ^  Thus  A.  ^1200 

B.  600 

C.  700 


Then  as  2400 
as  2400 
as  2400 


Whole  debt  ^2400 


1200 
600 
700 


125=D.'s  ] 

100=:E.'S 

75=F.'s  ^ 


Ans. 


1800 
1800 
1800 


900 
375 
525 


Ans 


j^lSOO  proof. 


(4)         Thus  A.  had  50  ca«/c. 

B.  80 

C.  70 

Sum  200 


cattle,  cattle. 
Then  as  200  ;  60 
as  200  :  80 
as  200  :  70 


$60  proof. 


(5) 


FELLOWSHIP. 

$ 

Thus,  to  A.  120 

B.  250  75 

C.  300 

D.  208  25 

Sum  879  00 


117 


Then  j 

As  j5879  :  g650. 


$ 

120  :  88  754-=A.'ssh. 
250  75  :  185  42+  =:B.'s  sh. 
300  :  221  84+  =C.'8  sh. 
208  25  :  153  99+  =D.'6  sh. 


■  Ans. 


(6)        Thus  A.  is  to  have  1  portion. 

B.  2 

C.  6 


9  sum  of  the  portions. 


Then  as 


900  :  lOOrrrA.'s  share. 
900  :  200=B.'8  share. 
900  :  600=C.'s  share 


ii 


Ans. 


(7)     Thug,  he  owes  to  A.  250  50 

B.  500  00 

C.  349  50 


Sum  1100  00 


Then 

As  1100  :  960 


$     cis.  f     cts.m. 

[250  50  :  213  61    8+  A.'s  ; 

500  00  :  436  36  3+  B.'s 

[  349  50  :  305  01  8+  C.'s  ' 


Ans. 


1  1^  FELLOWSiriP. 

EXAMPLES 

CASE  2. 

% 
(1)  Thus    8«X3=  264 

120X4—  480 
300X6=1800 

Sum  of  stocks  and  time  2544 

%  i         i   cts.m, 

C    264  :  ;  184  :     19  09  4=L.'s   ) 
Then  as  ^2544  :  \    480  :  •,.  184  ;    34  71  6=M.'s  >  Ans. 
(  1800  :  :  184  :  130  18  8=N.'s  ) 

$      m.       $  .  $      m.      ^ 

(2)      580X3=1^740  480x3=1458 

+  100  —300 

680X9=6120  180X2=372 

+500 

A.'s  product  78fJ0  

686X3=2058 

%      m.       $  —400 

1000X9=9000  

+  200  286Xl=:286 

+  1000 

1286X3:=3858 

C.'s  product  8032 

% 
A.'s     78<50 
B.'s   12600 
C.'s     8032  g  ^    cU.m, 

%      (tx.     C    7860  :  581   64  8+A  )  . 

28492  :  2108  44  ::}  12600  ;  932  41    4+B  >'^^^* 
.(    8032  :  594  37  7+C  ) 


1200X3=3600 


B.'s  product  12600 


EXCHANGE.  119 

EXCHANGE. 

DOMESTIC  EXCHANGE. 

(1)  Thus,  £63  Us,  6d.~152Ud~T2d.  a  dollar  in  Vir- 

ginia=:^212  4lJc<*.     Ane. 

(2)  Thus,  £230  10^.   'rd.=5532'7d.~9Gd,    a  dollar' in 

New  York  and  N.  Carolina=g576  S2cts,  2m.  Ans. 

(3)  Thus,  ^150 

90^.=a  doll.  Penn.  cur. 


12)13500^. 

2|0)112|r> 

£56  5.9.     Ans. 


(4)  Thus,  ^377  40ds. 

72c?. =a  doll.  Mass.  cur. 


754  80 
26418  0 

12)27172  80 

2j0)225|i  4d, 

£113  4;?.  4d.  Ans. 


(5)        ^      Thus,  g389  45cts'. 

56<i.=a  doll,  in  Georgia. 

233670 
194725 

12)21 809J20 

2|0)181j7  5 


£90  17*.  5d,  Ans. 


120  EXOHAKGE, 

FOREIGN  EXCHANGE. 

EXAMPLES. 

(2)  Thus    £1  :  je76    ;:    $i  10cts,=^£l  li'ish  :  ^311  60 
cts.     Ans. 

(3)  Thus    gl  24cig.  ~  1  milrea  :  g532  Stids.    :  :   Im.  : 
429m.  298recw.-f     Aus. 

(4)  Thus  eCcts.  :  gl869  :  :  Iru.  :  283i^rw.     Ans. 

(5)  Thus  1^,  :  ie5g,  :  :  39dJ.  :  g64  35c^*.     Ans. 

(6)  Thus  33c<*.  5m.=lm.  b,  :  §280  58cfe.  5wi.  :  :  Im.  6. 
:  837m.  6.-f-     Ans. 

(7)  Thus   1/i  :  562/i.   :  :   18d^.  5m.=l/j.  :  gl03  97ds. 

Ans. 

(8)  Thus  \0ct8.=zlriai plate  :  ^463  :  :   Irial  :  4630ria/5. 

Ans. 

(9)  Thus  Ijfo.  :  40cts,  :  :  591/o.  17*^  :  §236  74ds. 
Or  1«^  :  2d*.  :  :  591^0.  17*^  :  §236  74f<5. 

Then    §100  :  §160    ::  §236  74d5.  :  §378  78^*.+ 
Ans. 

(10)  Thus  as  100cr.+25  :  1005.  :  ;  2464m.  6.  :  1971m.  6. 

3sch.  2^pcn.     Ans. 

(1 1)  Thus  Icr.  :  32-if/.  : :  2000cr.  :  £270  16*.  Sd.  Ans. 

(12)  Thus  as  lpi.~Sri,  ;  366?.  ;;  §1676  6ri.=:16766r/. 

;  £314  7*.  a^.     Ans. 

(13)  Thus  lpez.=20sol.  :  54d.  :  :  ^MOpez,  l5soL  :  £886 

13*.  41(1,     Ans. 

(14)  Thus  \ru.  :  4*.  3d  : :  2586rw.  :  £549  10*.  6d.  Ans. 

(15)  First  £1   :  £450  15*.  :  :  34*.  6rf.  1866104/?fnrp. 
Or  20*.   :  9015*.  :  :  414rf.  :  1 866  lO^pencc  Flemish, 

or  groots. 
Then  50*^=100^.  :  ISeeiO^d.  : :  Iru.  :  1866n/.  10-^ 
cop.     Ans. 

(16)  Thus  as  £io8  6*.  Hd,  Irish  :  £100*<^.  :  :  £813  3* 

6d.  :  £750  12*.  6d.  Sterhng:.     Ans. 


VULGAR   FRACTIONS.  121 

(17)  First  20*.  :  33*.  Qd.  ::5s,:  Ss,  4U. 

Then  5*.  :  8*.  4|(/.  :  :  32i^.  :  54^d.  Flemish.    Ans. 

18)  Thus  32ld.  :  54^d.  i  :  5s,  :  Ss.  4ld. 

Then  as '5*.  :  8*.  4^d,  :  :  20*.  :  33**.  6c?.     Ans. 
*.     *.  d, 

(ig)  Thus  |5|||33  6 

8  4|=value  of  a  crown  at  that  rate. 
Then  8*.  4lrf.  :  6*.  :  ;  54fjC?.  :  32|(/.     Ans. 

(20)  Thus  32»ff.  :  32c?.  :  :  36*.  Gd,  :  36*.  2|f f?.     Ans. 

(21)  Thus  51c?.  :  53c?.  :  :  42c/.  :  4S}]d.     Ans. 

VULGAR  FRACTIONS. 

REDUCTION  OF  VULGAR  FRACTIONS. 

EXAMPLES. 
C*ASE    1. 

(2)  Numer.  108)144(1 

108 

Common  measure  36)108(3 
108 

Then  36)i^|=f .    Ans. 

(4)  Numer.  126)234(1 

126 

108)126(1 
108 

Common  measure    18)108(6 
108 

Then  18)lSf=f3.     Ans. 


122  VULGAR    FRACTIONS. 

CASE  2. 

(2)  45X34-2=i|'7.     Ans. 

(3)  Thus  1564X5-f3='7s^23,     ^ns. 

CASE  3. 

(2)  Thus  67-r-7=94.     Ans. 

(3)  Thus  1 6)364(22  j|.     Ans. 
32 

44 
32 

''       12 


CASE  4. 

(2)  Thus  6X8X11X13==6864  numer._^72_.    .   ^ 
And  7X9X12X17=12852  denom.     '"*' 

(3)  '    Thus  7X15X8X6=5040  numer._^4oo       ^^g 
And  12 X 19  X 1 1 X  13=32604  denom.     ^^^* 

CASE  5. 
(2)        Thus  5)5  20  10  15  the  denominators. 

2)1     4     2    3 

12     13 


Then  5  x  2  x  1  X  2  x  1  X  3=60  common  dcnom. 

Then  the  com.  denom.  60—5=12X4=48^ 

60-r  20=3  X  9=27  I  „„^^^ 
60-4-10=6x7=42  f""""^^' 
60—15=4X4=16] 

That  is  fl  iJ  41  U'     Ans. 


VULGAR  FRACTIONS.  123 

(3)  Thus  2)10  2  9  the  denom. 

5  19 


Then  2x 5 x  1 X  9=90  common  denom. 
90-r-10=  9X9=81) 
90~-  2=45  X  1=45  >  numer. 
90-f-  9=10X5=50) 

ThatisJJ^fJ.     Ans. 

CASE  S. 

^2)  First  lib.  troy=240t?io«.  therefore  |  of  aiir=x2T?F= 
;f^a.    Ans. 

(3)  Thus  3xlXl_  3        Anc? 
And     8x4x4-~^^-     ^'^• 

(4)  Thus  lkhd,=:SO^ts,  therefore  |  of  shF^iwsJ''^^' 

Ans. 

(5)  Thus  8/«r.=lm.  therefore  9x1=9  the  numer.  and 

16  X  8=128  the  denom.=y|^.    Ans. 

CASE  7. 

(2)  Thus  2X112=224  the  numer.  and  252x1=252  the 

denom.=f||=|/6.     Ana. 

(3)  tIht  of  £l=Tifff^  of  ^r  ==l^ll=^^-     Ans. 

CASE  8 

(2)  Thus  J  of  a  Bhilling=5  of  y=y =10|(/.     Ans. 

(3)  Thus  If  of  a  day=||  of  \^—%\^—^hrs.    Ans. 

(4)  Thus  fg.  of  an  acre=TV  of  |  of  |-''=Vi"  perches= 

Ir.  lOp.     Ans. 

CASE  9. 
(2)  Thus  bs.  4^.=64J.  and  £l=240<^.  therefore  4\= 
y\£.     Ans. 


124  VULGAR  Fractions. 

(3)  Thus  Cmo.   2w.=26iv,  and  lyr.=52w.  therefore  || 

oriyr.=:|yr.     Ans, 

(4)  Thus  2qrs.  3/i«.=llna.   and  lijd,=^16na,  therefore 

j}yd.  is  the  Ans. 

ADDITION  OF  VULGAR  FRACTIONS. 

EXAMPLES. 

(2)  Thus  t\+A+A+tV=H=1-    Ans. 

(3)  Thus  44-.iJ-f  «=V=16.     Ans. 

(4)  Thus  6)5  10 

1    2=10  common  denom. 
And  10—  5X2=4) 

10-10X5=5  P^"'^^- 
Whence  A+tV^A-     Ans. 

(5)  Thus  3|=V,   8f=V%   and  4x7x9==252  common 

denom. 

And  252—4X13=  819) 

252—7x58=2088  >numer. 

252-^-9  X    4=  112) 
Whence  fH+WI+Ht='¥7?l=ll|H-     Ans. 

(6)  Thus  i  of  |=H=A.  andf  of  t^=^=/,. 
Then  8)16  24 

2    3=48  common  denom. 
And  48^16X5=15)    „^^^ 

48-^24x7=14  r 
Whence  4f+i|=o.     Ans. 

(7)  Thus  iof -fof  Y=»|«=53'per.=Ir.  13Jp. 
And  ^  of  V«=2f-«=28j[>. 

Whence  \R.  13j/>. 
0     28 

Ans.  2        U 


VULGAR  FRACTIONS.  125[ 

MULTIPLICATION  OF  VULGAR  FRACTIONS. 

EXAMPLES. 

(2)  ^  by  1  thus  2X  1=2__  ^ 

(3)  Thus  6|=:26  by  i=26xl^26_ 

4X7=28" 

(4)  4f=V^  by  f=19X2=38_ 


-=--y^.     Ans. 


4X3=12^^^=-^-     ^"^- 


SUBTRACTION  OF  VULGAR  FRACTIONS. 

EXAMPLES. 

(2)  Thus  ^  of  1=0^  whence  ^J— Jg. 
4)20  28 

5     7=140  common  denom. 

140—20x10=133. 

V  numer. 


19=133  > 
1=     5[- 


140-f-28X 

wnence  y^-jy — jaq — to — a?*     -^"S* 

(3)  Thus  1X14=:  14  common  denom. 
And  14-^   1X5=70) 

14-14x8=  8  r"^"""'- 
Whence  1^—^^=:Y^=4{^,     Ans. 

(4)  Thus  I  of  a  league=|  of  3  miles=2  miles. 

And  -^  of  a  mile=  7jf  of  8  furlongs=:|^'==5-^  fur- 

longs=:5  furlong's  24  poles. 
Therefore  2m. — 5fur,  24/>o.=lm.  S/wr.  IGpo,     i\ns. 

(5)  Thus  5|='^3  and  2|=|  therefore  4x3=12  com.  d. 
And  12-f-4x  23=89) 

12-f-3X   8=32  r'"'''^'' 
Whence  f|— f|=ft=3^.     Ans. 

(6)  Thus  2  of  "^^=1-1  and  |  of  |=|^. 
And  4)48  20 

12    5=240  common  denom. 
And  240~.48X  14=70  ) 

240-20  X   3=36  P™^^*- 

70  3  0   3  4    17  A  «« 

2Tff 2¥0 24^ T2  0*        -^"S* 


126  VULGAR  FRACTIONS. 

DIVISION  OF  VULGAR  FRACTIONS. 

EXAMPLES. 

(2)|by?tIiusJ)f(5V     Ans. 

(3)  6|=^/-^lthusa)3J3(9/r=l9|.    Ans. 

(4)  Thus  f  of  1=-^  and  1  of  |=f. 
Then  T^-H|  thus  |)^tM='l-     Ans. 

(5)^byfthus4)i(TV=f.     Ans. 

(6)|ofi=iJand|of|=5V 

Then  4J  by  J,  thus  |')J-KW=16f  Ans. 

(7)  1  of  17i=i  of  \'=^\'.     - 
Then  =y5-^1thus-J)-V(V2=llj.     Ans. 

(8)  Thus  f  of  91.p=.|  of  ^ry'^^f?!^- 

And  l^i'^'if  thus  i^i^'nV{\\m^=3i^Uif 
Ans. 

RULE  OF  THREE  IN  VULGAR  FRACTIONS. 

EXAMPLE.?. 

(2)  Thus  3l.yds.=\^  and  9j.9.=|-9  and  ^7jds.=Y' 
Then  we  have  V  =  l""  =  =  '/  =  l^*-  3</. 

For  3,0  X  V^=:lV5:~^\=|'iV=l  4..  3^.     Ans. 

(3)  Thus  I  :  20  .  .  3  .  121/J.s'. 

(4)  Thus 273 x4/)e.=llly(Zs.  ^nd  15§«.~16«.  8</. 
Then  say  as  in  whole  numbers,  lyd,  :  lllyrf*.  :  :  15*. 

ad,  :  £86   19 J. 
For   13*.  8J.=:188c?.xllli/(Z5.=20868(f.  which -7-12 
-r20=£86  19*.     Ans. 

(5)  Thus  55ci/?<.=V  fi^nd  £3m=»5»«. 

Then  we  have  =-V»  :  §  :  :  »5-f«  :  £2  6*.  3||<i. 

1  or      50    A  y  —   jffjy  ~5g  — -  BO^ff  X.  —  **^  0*.   Jyfa. 

Ans. 


DECIMAL  FRxVCTIOXS. 

(6)  First  lf/6.=|. 

Then  J^/6.  :  |/6.  :  :  ^oL  :  $2  '74^cts, 


127 


For^ 


$2  74^ds,     Ans, 


(7)  Thus  20f(Z.=r:«2. 

Then  inversely  thus  6m.  :  10m.  :  :  V^day,  :  S4Mays 
For  «^2  X  Y  =  ^^-r-l=:^\%'—'^4±days.     Ans. 

(8)  First  ^  of  2lcv'f.=i  of  |=f  of  a  cwt 

Then  this  reduced  to  lbs",  would  be  |  of  *l2_.56o^ 
Then  we  have  6llbs.=  \p  :  s.^o  .  .  3  .  ^q  76||^-;^. 
For  ^f^Xf^^ll^H-f^^l^f  £^o/.=glO  7611^;?. 


DECIMAL  FRACTIONS 

ADDITION  OF  DECIMAI.S. 

EXAMPLES. 


(5) 


56.12 
.7 

1.314 
6837.01 
.15 


Ans.  5895.294 


(6) 


361.04 
.120 
78.0006 
101.54 
8.943 
.3 


Ans.  549.9436 


(2) 


MULTIPLICATION  OF  DECIMALS. 

EXAMPLES. 

(3)         4560. 


54.20 
38.63 


16260 
32520 
43360 
16260 

Ans.  2093.7460 


.3720 

91200 
31920 
13680 

Ans.  1696.3200 


li^ 


1^8  DECIMAL  FRACTIOKS. 

(4)  .28043 

;0005 


Ans.  .000140215 


SUBTRACTION  OF  DECIMALS. 

EXAMPLES. 

(5)  13.16421  (6)         5960. 

4.286  .3742 


Ana.     6.87821  Ans.  5959.6258 


DIVISION  OF  DECIMALS. 

EXAMPLES. 

(2)     4.20)148-63(35.304+     Ans. 
1263 


2233 
2105 
(4)     931.)2.00385(.0021523-f-  Ans, 

1280  1862 

1263  


1418 


1700  931 

1684  

4875 

16  rem.  4655 


(3)     3.2).2142(.066-f     Ans.  2200 

192  1862 


222  3380 

192  2793 

30  rem.  587  rem. 

"■     II     I       <l ■> I  ■mil 


DECIHAL  FRACTIONS.                               129 

REDUCTION  OF  DECIMALS. 

CASE  1. 

(2)         8)7.000 

(3) 

24)170(.70833+ 
168 

.875  Ana. 

200 

192 

80 

•72 

80 

72 

•— 

8  rem. 

(4)  2162.)3810(.1762+  Ans. 
2162 

(5)254)1160(.4566+ Ans. 
1016 

1440 

16480 

15134 

1270 
1700 

13460 

12972 

1524 

4880 

1760 

4324 

1524 

556  rem. 

236  rem. 

■■si.      ,  .1  ■            ■■  ■■■Ja 

130 

DECIMAL  FRACTIOIiS. 

CASE  2. 

(2) 

Thus  2i2.  4P.=84P.             lwi.=160P. 
Then  160)840(.525    Ads. 
800 

400 

320 

800 

800 

(3) 

2qr.  2na,=zlQm, 

Then  16)100(.625 
>96 

40 
32 

80 
80 

And  lyd.=zl6na, 
Ans. 

(4) 

Ur.=:60wim.             And 

60)5.00(.08333-f     Ans 
480 

(3)     lo2r.=480^r*. 

Then  480)1 000(.02083-l-  Ans. 
960 

200 
180 

4000 

200 

3840 

180 

1600 

200 

1440 

180 

160  rem. 

20  rem. 

DECIMAL   FRACTIONS.  131 

(6)     2qts,  \pl.—5pts, 

lhhd,=::S04pts,    Then  504)5000(.1to992-f     Ans. 
4o36 

4640 
4536 


1040 
1008 


32  rem. 


CASE  3. 

£                               Day.  GaL 

(2)     .1361                      (3)     .235  (4)     .42 

20                                24  4 


«.2.7220  940  ^f.l.GS 

12  470  2 


qt,pt. 

<Z.8.6640  7ir5.5.640         jp^.1.36  Ans.  1  1.36 

4  s,d,  60  

Ans.  2  84- 

5r.2.6560         — ^mm.38.400 

60 


■  A»v.  min*  sec, 

5ec.24.000  Ans.  5     38    24 


s.                              Yd,  Acre, 

(5)  .253                   (6)     .436  (7)     .9 

12                                 4  4 

J.3.036Ans.3.036  ^r.1.744  r.3.6 

4  40 

qr.  na,     '  Jt,  P. 

wcf.2.976  Ans.  1    2    ;?.24.0  Ans.  3  24 


132 


POSITION. 


RULE  OF  THREE  IN  DECIMALS. 

EXAMPLES. 

(2)  Thus  lAyd.  :  IS.yd,  :  :  13*.  :  £6  19s,  3d.  l.Tljr. 
For  13X15=195.  the  dividend. 

Then  195.-t"1.4=£6  19*.  3^.719^     Ans. 

(3)  Thus  \qr,  :  1yd,  :  :  p  M.5cts.  :  p  2Qcte. 
For  2.  34.5x4—^9  ^Sds,     Ans. 

(4)  First  sold  it  for  pOS.SOds, 

but  paid  for  it        84.39.12— 

gained  on  it        g23.90.88 

Then  W.5cwL  :  Icwt,  :  :  g23  90d*.  88m.  :  $2  21  ds, 

7m.  + 
For  23  .90  88-r10.5=|j2  27d*.  7m.     Ans. 

(5)  Thus  ^20.8  :  ^2.6  :  :  2i0pie,  :   145.38/we.+ 

For  240X12.6=3024.0  which  —20.8=1 45.38pie.+ 
Ans. 

(6)  Thus  S,Soz.  •:  5.2o^.  :  :  '74.6d*.  :  gl   lOcfe.  8m. 
For  5.2x74.6-^3.5=^1  lOds.  8m.    Ans. 

POSITION. 

SINGLE  POSITION.  : 

EXAMPLES. 

i 

(2)    Suppose  162  in  the  box. 


32.40=J 
27.00=*; 
20.25=J 
13.50=jV 


Result  93.15 


Theng93  15ds.  :  gl62  ::  |J690  :  jjl200.     Ans. 


POSITIO?f. 


133 


(3)    Suppose  C.'s  40 
+  8 


+  16 

64r=A.'s 
48=B.'s 
40=C.'s 

152  result. 


Then  n2yrs. 


yrs.  yrs,    yrs. 

(64  ::  133  :  56r=A.'s  ) 

.  :    J48  ::  133  :  42=:B.'s  >Ang. 

(  40  :  :  133  :  35=C.'s  ) 


133  proof. 


(4)     Suppose  No.  3  cost  20 
3 


60=No.  2. 


120= No.  1. 
60 
20 


Result  200 


Then  200  : 


350  :  2lO=No.  1. 
350  :  105=No 
350  :     35= No, 


Ans. 


M 


134  POSITION 

Yrs, 
(5)        Suppose  60 
2 

120 
3 

5)360 

3)72 

24  result. 

Then  242/r5.  :  GOyrs,  :  :  14yr$.  :  35yrs,     Ans. 

£ 

(6)        Thus  suppose  40 

200 
20 
10 


T  *   r     1  20 

Int.  for  1  yr.  < 

[«.6|00 


Then  as  £10  14*.  8rf.  :  £201  5*.  :  :  £40  :  £750.  Ans. 
£    s. 
And  \l\2    6 

4  years. 


Int.  in  4  yrs.  9     4 
3 

7     8 


Int.  for  8  mo.  \  pj^    ^ 


Whole  int.  10  14    8 


•^  < 


(7)  Thus,  suppose  the  cistern  to  hold  100  gallons.  i 

Then  100-^ 45min.=2^^aL=ihe  quantity  which  the' 
first  cock  discharges  in  a  minute. 

And  W0-^55min.=^l^jgal,  the  quantity  which  the 
second  cock  discharges  in  Imin. 

Then  100-^30mm.=3^^a/.=the  quantity  which  the 
discharging  cock  discharges  in  Imin.  Consequent- 
ly, 2^gaL^l-fjgaL=4^^gaL  the  quantity  which 
the  cistern  receives  by  both  the  first  and  second 
cocks  in  a  minute.  Then  as  2igals,  run  out  in  the 
same  time,  ^r^gctl. — S^a/.^jfg-aZ.  that  the  cistern 
gains  in  Iwim. 

Then  l^gaL  :  lOOgaL  : :  1mm.  :  2^^^,  21nii7i.  25 f see. 
Ans. 


DOUBLE  POSITIO.V. 


(2)    First  suppose  they  received  276 


3)552 

184=:what  A.  spoiU. 
-i-250 

434=:what  B.  spent. 
—276 

1 58  B.  w^as  in  debt  every 
7  year. 

1106=7  years'  debt. 
—350 

756  error  too  much. 


136  POSITION. 

Again  suppose  the  salary  was  300 

2 

3)600 

200=A.  spent. 
J- 250 

450  B.  spent. 
•—300 

B.  was  every  year  1 50  in  debt. 
7 

And  in  7  years  he  was  1 050  in  debt. 
--350 

700  error  too  much. 

Then  756  X  300=226800 
700X276=193200 


Difference  of  errors     56)33600(^600  the  salary,  f 
336  of  which=400 

A.'s  share,  then 

00       400+250=650 
B.'s  share.  Ans. 

(3)        First  suppose  30  working  days. 

§30 
— 10  that  he  forfeits. 

Tlcceivcs  20 

27  50 


7  50  error  too  little. 


137 


Again  suppose  20  worldng  days. 

Forfeits  15 

Receives    5 

27  50 

22  50  error  too  little. 

Then  2250x30=67500 
750X20=15000 

Difference  of  errors  1500)52500(35  workino-  days. 
4500 

7500 
7500 


Therefore  50 — 35=15  idle  days.     Aiis. 

$ 

(4)     First  suppose  10  cow6=160 

And  10  oxen=240 

40  calves=240 

The  whole  640 
—320 


320  error  too  much. 


Again  suppose  8  cows==12S 

And  8  oxen=:192 

And32calves=192 

The  whole  512 
320 


192  error  too  much. 


138  rosiTio:N'. 

Then  320x8=2560 
192X10=1920 

DiiFerence  of  errors  12S)640{5cows    boxen   &   ^Ocaltes. 
640  Ans. 


(5)    First  suppose  Again  suppose 

Ft,  Ft, 

No.  2=20  No.  2=30 


10=1  i5=i 

15  15 

25=No.  3.  30=No.  3. 

4-15  +15 

40  45=No.  2. 

—20  —30 

20  error  too  much.      15  error  too  mucli. 


Tiicn  20x30=000 
15X20=300 

Difference  of  errors  5)300 

60=No.  2,  then  60—15=45= 
—  No.  3. 

And  then  we  have  No.  1=15,  No.  2=60,  and  No. 
3=35,  which  added  together=  120/1.  the  length  of 
tht;  pole.     Ans. 


rosiTiox.  139 

(6)  Thus  first  suppose  the  whole  property  to  have  been 
worth  jS  £ 

396  Again  suppose  432 


198=1 

216=; 

—40 

—40 

158= A. 's  share. 

176=A.'8 

132=^ 

144=1 

+  12 

+  12 

144=B.'s  share. 

156=B.'3 

—80 

—80 

60=C.'s  share. 

76=C.'s 

144 

156 

^58 

176 

366  sum. 

408  sura. 

396 

432 

30  error  of  defect.  24  error  of  defect. 


Then  432X30=12960 
396X24=  9504 


Difference  of  errors  6)3456 

£576  Ans. 


£ 

Then  576-^2—40=248  A.'s  share. 
204-r-3-f  12=204  B.'s    do. 
204—80=124  C.'s    do. 


£576  proof. 


140                                            POSITION. 

(7)    First  supDOse  each  boy  received  3 

2 

6  =  share  of  each 

3        woman. 

18=  share  of  each 

—          man. 

And  19X3=  67 

11X6=  66 

7X18=126 

249 

172  19  4J^                                       1 

76 

0  7 J-  error  of  excess.        j 

£ 

Again  suppose  each  boy  received  1 

2 

2  share  of  each  woman. 

3 

6  share  of  each  man. 

£ 

And  19X1=19 

11X2=22 

7X6=42 

83 

172  19  4J                                         1 

09  19 

4J.  error  of  defect.          1 

, , ^ J| 

INVOLUTION  AKJ)  EVOLUTION .  141 

£,    S.    d. 

Now  89  19  4|X3=2G9  18  0] 
76     0  7JXl=  76     0  7J 


345   18  8i 


Which  -—166  sum  of  errors=:=jG2  1*.  8c?. -|-  =each 
boy's  ehare,  which  X2=:JC4  35.  4|(/.4-  =each 
woman's  share,  which X3=jei2  10^.  OJd!.-f  = 
each  man's  share.     Ans. 

INVOLUTION,  OR  THE  RAISING  OF 
POWERS. 

EXAMPLES. 

(2)  14X14X14=:2744.     Ans. 

(3)  2.8X2.8X2.8X2.8X2.8X2.8=:4S1. 890304.     Ans. 

(4)  .263X.263X.263=.013191447.     Ans. 

(5)  }XiXiX|XiXjXiXi=^7i^^.     Ans. 

(6)  401x401x401x401—25850961601.     Ans 

EVOLUTION,  OR  THE  EXTRACT- 
ING  OF  ROOTS. 

SQUARE  ROOT. 

EXAMPLES. 

(2)  39375655(6275  Ans.       (3)  14C6.179010(38.5o.  Ans. 
36  9 

122)337  68)586 

244  644 


1247)9356  765)4217 

8729  3825 


12545)62755  7705)39290 

62725  38525 


Rem.    30  Rem.   76510 


142                                     SQUARE  ROOT.                                                1 

(4)  ^6385163(9817  Ans 
81 

(^) 

.0001 324960(.01 151  Ans. 
1 

188)1538 
1504 

21)32 
21 

1961)3451 
1961 

225)1149 
1125 

19627)149063 
137389 

2301)2460 
2301 

Rem.  11674 

Rem.  159 

1 

(6)         18.362147(4. 
16 

285     Ans. 

82)236 
164 

848)7221 
6784 

8565)43747 
42825 

Rem.    i     : 

(^)    15^5=,!'  •"-  ^' a^iarc  root  is  J.     Ans. 

(8)     36)1?-=- whose 

square 

root  is  ^.     Ans. 

SQUARE  ROOT.  143 

(9)     500)3200(v^64(.8  Ans.          (10)  50x64-f  49=:3|4  9, 
3000      64 

-; Then  3249(V=7J.     Ans. 

2000  25 

2000  

107).749 

749 

And  \/. 6 4f. 8  denominator. 
64 


(11)     30x100+25=30.23  (12)     1296(36     Ans. 

3X3=9 

Then  30.25(5.5=5-,%.  Ans.                 

25  66)396 

396 

105)525  

525 


(.13)     169(13     Ans.  (14)     3097600(1760ydf^.=lmi/€. 

1  1  Ans. 

23)69  27)209 

69  189 

346)2076 
2076 

00 


b 


144  SQUARE  ROOT. 

(15)  Thus  15X15=225 

24X24=576 


V^801(28.3ft.An«. 
4 

48)401 
284 


563)1700 
1689 

Rem.  11 


(16)  212X212=44944/^. 

And  202/<?*.=6OX60=  2600/1, 


41344(203.332/?.     Ana. 
2X2=4 

403)1344 
1209 


4003)13500 
12189 


40663)131100 
121989 


406662)911100 
813324 


Rem.  97776 


CUBE  ROOT.  145 

CUBE  ROOT. 

EXAMPLES. 

(2)  7532641(196.1)2    Ans. 

1 

{  Defec.  div.  and  squ.  of  9=381    6532 
^+270=:com.  divisor         =651    6859 


5  Def.  div.  and  squ.  of  6=108336    673641 
^ +3420=com.  div.        =111756    670536 


Defective  divisor     115248  3105000 


;Def.  di.  «fe  sq.  of  .02=1152480004)3105000000 
I  4- 11760  =  com.  div.  =1152491764)2304983528 

Rem.  800016472 


(3)  12.113847500(2.296     Ans. 

2X2X2=3 

;  Def.  div.  and  sq.  of  2=1204)4113 
»  +120  =  com.  divisor  =  1324)2648 


5  Def.  div.  &  sq.  of  9=145281)1465847 
(+5940  =  com.  di.  =  151221)1360989 


5  Def.  di.  &  sq.  of  6=15732336)104858500 
(  + 61830  =  c.  di.  =  15773556)  94641336 

Rem.  10217164 


146  CUBE  ROOT. 

(4)  5382674(175.2     Ans. 

1 

5  Defec.  div.  &  square  of  7=349)4382 
(  -f  210=complete  divisor     =559)3913 


J  Defec.  div.  «&  square  of  5=86725)469674 
I  -f  2550=:completc  divisor=89275)446375 


J  Defec.  div.  &  squ.  of  2=9187504^23299000 
I  -f  10500  =  com.  divisor  =9198004)18396008 

>Rein.  4902992 


(5)  .378621 350(.723.     Ans. 

7X7X7=343 


J  Defec.  div.  &  sq.  of  2=14704)35621 
^4-420  =  com.   divisor  =15124)30248 


J  Defec.  div.  &  sq.  of  3=1555209)5373350 
(  -f  6480=com.  divisor  =1561689)4685067 

Rem.  688283 


(6)  46.295363543(3.590    Ans. 

3X3X3=27 


J  Def.  div.  &  sq.  of  5=2725)19295 
I  4-450=com.  divisor=3 175)  15875 


J  Def.  div.  &  sq.  of  9=367581)3420363 
J +9450  =  com.  di.  t=377031)3396279 


Defective  divisor    1 2888 1  )24084543 


ALLIGATION. 

147 

(7)    Thus4)X«|5= 
.2007722 

J  Defec.  divis.  &  S( 
( -f  200=complete 

5  Defec.  div.  and  sq 
14-8700  =  com.  di 

(8)            Thus 

=23%>  which  reduced  to  a  decii 

Then  .200772200(.585 
125 

[nal= 
Ans. 

Ans. 

ju.  of  8=7564)75772 
divisor  =  8764)701 12 

.of  5=1009225)5660200 
visor=  1017925)5089625 

570575  Rem 

;j/36.|«=V36.8666664-(3.32 
3X3X3=27 

5  Defec. 
I  4-270= 

div.  &  sqi 
=complete 

1.  of  3=2709)9866 
divi.  =2979)8937 

5  Defec. 
14-198: 

div.  &  sq. 
=  com.  div 

of  2=32i?704)929666 
isor  =328684)657368 

Rem.  272298 

^9®9^ 

ALLIGATION. 

CASE  1. 

(2) 

Cwt, 
2  a 
4 
7 

13 

$  cts.          $  ds. 
t  25         =50  00 
20  50  =  82  00 
18  621=130  37^ 

g262  371 

Then  as 
Ans. 

newt.   : 

UwL   :•,   $262  ^71^^.    :    $20 

I8jd*. 

148 


ALLIGATION'. 


(2) 
Mean  rate  50 


CASE  2. 


=36  at    34  cts.  ^ 
=60  at    42  cts.  I    . 
=  16  at    86  cts.  f^^^' 
=  8  at  110  cts.  J 


CASE  3. 


(2) 

Mean  rate  92 


Then 


86  cts. 
94  cts 


18  at  105  cts 


'^ 


Ans. 


CASE  4. 


(2) 
Mean  rate  145 


Then  as  80  :  50 
80  :  15 
80  :   15 


32 

32 
32 


80  sum.  of  difter. 


20  at  130  cts, 
6  at  160  cts 
6  at  180  cts 


i:| 


Ans. 


ARITHMETICAL  PROGRESSION.  149 

AFJTHMETICAL  PROGRESSION. 

CASE  1. 

EXAMPLES. 

(2)    Thus  40—1=39  (3)     10—1=9 

2  com.  dif.  4  com.  dif. 

78  36 

2=  1st  term.  +10=^lst  term. 

80  1st  Ans.  46  last  term. 

2=  let  term.  -flO 

82  sum.  56 

40  10 

2)3280  2)560 

gl6.40  Ans.  280  2d  Ans. 


(4)  75—1=74 

2  common  difference. 

148 

-f  6= 1st  term.  ^ 

^1.54  for  the  last*    Ist  Ans. 
6= 1st  term. 

160  sum. 
75 

800 
1120 


2)12000 


00  in  the  whole.    Ane. 


^  2 


150  ARITHMETICAL  PKOGRESSION. 

CASE  2. 

(2)  Thus  175 

—21 

8—1=7)154  . 

jj22  common  difference. 

And  175+21=196  sum  of  extremes. 
8  number  of  terms* 

2)1568 

784  whole  sum. 

Lastly  21-1-22=  43=2d  payment. 

43+22=  65=3d 

65+22=  87=4th 

87+22=109=5th 

09+22=131=6th 
131  +  22=153=7th 
153+22=175=8th 

763 
21= 1st  payment. 


$784  proof. 


(3)    Thus  49  Then  49+4=53  sum  of  extremes. 

-—4  10  number  of  terms. 

10— .1=9)45  2)530 

5com.  dif.   Received  $2.65    Ans. 


GEOMETRICAL  TROGRESSION.  151 

GEOMETRICAL  PROGRESSION. 

EXAMPLES. 

(2)    Thus  power  12     3      4 
Ratio  3     9    27    81 

27  3d  power 

"567 
162 

2187=7th  power. 
5= 1st  term. 

l6t  Ans.  10935=:last  term. 
3  ratio. 

32805 
— 5= 1st  term. 


Ratio  less  1=2)32800 


jei6400    Ans.  2nd 


(3)  Thus  power  1234567      8      9 
Ratio  2  4  8  16  32  64  128  256  512 

512 

1024 
512 

*  2560 


262 144=  18th  p. 
4=2d  do. 


1048576=20th  p. 
1  1st  term. 


1048576=lastt. 
2  ratio. 


2097152 

l  =  lstt. 


Ratio  less  1=1)2097151 

Ans.    g20971.51c<r 


152  COMPOUND  INTEREST  BY  DECI]>LA.LS. 

COMPOUND  INTEREST  BY 
DECIMALS. 

EXAMPLES. 

(2)    Thus,  tabular  number  1.2155062 

750 


607753100 
85085434 

911.6296500 
Amourtt  of  £1  for  6mo.        1.024695  from  table  first. 


45581482500 
82046668500 
5469777^000 
36465186000 
18232593000 
91162965000 

je934. 1423442067500 
20 

«.2.8468841350000 
12 

rf.  10. 1626096200000 


£  8,  d. 

Amount   934  2  10-}- 

Principal  750  0    0 

Interest  184  2  10+     Ans. 


ANNUITIES  AT  COMPOUND  INTEREST.  1 53 

CASE   2. 

(1)  Thus  £695  13*.  9d.=:695.6875£. 

Then  from  tab.  II.  1.2762815)695.68750(545je.  1*. 
9rf.-f     Ans. 

(2)  ThusjeseO  5«.  3<i.=260.2625je  which-rby  1.191016 

from  table  II.=£218  10*.  5d,+     Ans. 

ANNUITIES  AT  COMPOUND 
INTEREST. 

CASE  1. 

(2)    The  number  from  table  III.=5.637093 

200=annuity. 

Amount  for  yearly  payments=l  127.4186  which  X 
1.014781  proper  number  for  ^  yearly  payment  from 
table  V.=^l  144  08  2m.-{-  Ans. 

CASE  2. 

(2)    Thus,  the  num.  from  tab.  IV,=4.21236 

£70  annuity. 

^294  86  52  Ans.  for  y. 
payments. 

Then  jj!294.8652  X  1.014781  from  table  V.  = 
$299, 22.2-{- mills.     Ans.  for  i  yearly  payments. 

And  294.8652X1.022257  for  quarterly  payments 
from  the  same  table=^301.42.8-f  mi//#.  Ans.  for 
quarterly  payments. 


1 54  ,  COMBINATION. 

ANNUITIES  IN  REVERSION, 

(2)     Th^  9+4=13yo.=9^.98565  table  IV. 
4  do.=3.62989— . 


6.35576 
120 

1271152 
635576 


62.69.1.2m.  Ans. 


e@»44.~ 


PERPETUITIES  AT  COMPOUND 
INTEREST. 

(2)    Thus,  ratio— 1=1.06— 1=.06)260.00 


g4333.33.3m.-f     Ane. 

COMBINATION. 

EXAMPLES. 

(2)      Thus   20X19X18X17X16X15X14X13X12X1== 
1X2X3X4X5X6X7X8X9X10= 
670442572800 

. =  184756     Ans. 

3G28800 


DUODECIMALS. 

165 

PERMUTATION. 

EXAMPLES. 

(2)    Thus 

1X2X3X4X5X6X7X8X9X1C 
479001600  number  of  c 
15  seconds. 

X 11X12= 

tianges. 

2395008000 
479001600 

6|0)718502400|0  sec 

6|0)11975040|0  min. 

365AcZ.=8766  hrs.)l 995840(227  yrs.  248  days.  6  hrs. 
Ans. 

»mCQ9«»>». 

DUODECIMALS. 

ADDITION  OF  DUODECIMALS. 

EXAMPLES. 

Ft, 

(1)      10 
15 
18 
12 

in.  "   '"    ""                 Ft,  in,  " 
5     6  11     6          (2)     37     8  10 
9     5     2  10                   43  11     2 
4     17     9                    19     7     5 
8     6     5     7                   18     4     1 

///    ffff 

6  9 
4     7 
3     8 

7  2 

Ans.  57 

3    8    3     8      Ans.  119     7    7 

10     2 

1 

156  DUODECIMALS. 

Ft.  in.  " 

(3)  16  8  0 

14  6  0 

17  9  2 


Ans.  48  11     2 


SUBTRACTION  OF  DUODECIMALS. 

EXAMPLES. 

Ft,  in.    "    '"   ""  Ft.   in.   "    '"   "" 

(1)  From  38     8     4     7     5     (2)  From  720     3     8     1     6 

Take  15  11     6     9    3  Take    13     9     4     7  10 


Ans.  22     8  10     2    2  Ans.  706     6     3     5     8 


Ft.    in.   "    '"    "" 

(3)  From  475     7     2     0     0 

Take     81     2     5  10     6 


(2) 


Ans. 

394 

4      8      16 

MULTIPLICATION  OF  DUODECIMALS. 

CASE  1. 

EXAMPLES. 

Ft.  in. 
64  10 
5     7 

Ft.  in.  " 
(3)     6     9     3 

3     5 

31  11  10 
274     2 

2     9  10     3 
20     3     9 

306     1  JO 

Ans.  23     1     7    3 

(2) 
(3) 
sq. 

6 

1  - 

4"- 
1 

DUODECIMALS.                                       167 

CASE  2. 

Ft,  in,   " 
\      81   10     4 

7X2=14 

573     0     4 

2- 

1146     0     8 
J      40  11     2 
L        6     9  10     4 
»        2     3     3     5     4 
6     9   10     4 

1)1196     7     9     7     8 

is,l22     8     7     9     7     8     Ans. 

in, 

4 

1 

3" 
6//' 

1 

1 

I 

7 

^t.  in.  "    '"  . 
2     5     7     2 

}     9  10     4     8 
2     5     7     2 
7     4     9     6 
12     9     7 

9   10     4     8 
2     5     7     2 

ft.  1 

110     8     5     4  11  10  contents  of  Ish. 
10X10X10=1000 

10  10     7    0     6     1   10     4 
10 

108     9  10     5     1     6     7     4 
10 

1088     2     8     3     3     6     14    Ans. 

158  PROMISCUOUS  EXAMPLES. 


PROMISCUOUS  EXAMPLES. 


(1)  Thus  A.'s  25  years. 

+  15 

B.'s  40  years. 
+  12 

C.*s  52  years.    Ans. 


%      Cl8,  %     Cts, 

(2)    Thus  220  50-f-5=44  10  A.'s  own  share. 
220  50+6=36  75  B.'s         do. 


80  85  sura. 
220  60 


139  65=C.'s  own  share. 


^  ds.  j5  ds.m. 

Then  36  75+2=18  37  5=^  B.'s  share. 
44  10 


62  47  5=A.'s  last  share. 


^   els,  m. 
And     18  37     5 
139  65 


Ans.  158  02    5=C.'s  last  share. 


PROMISCUOUS  EXAMPLES.  159 

(3)     glcrO— g7l   :  poo  :  :   p6  25cts,  :  g60  Slds.  5m. 
-1-25. 
For  5625X100=562500  the  dividend. 
And  100—71=921  the  divisor. 
Then  562500— 92i=g60  Slots.  5?n.-f  25.     Ans. 


(4)    Thus  B.  gains  2  miles  per  hour. 

Then  as  2m.  :  50m.  :  :  Ihr,  :  25hrs.     1st  Ans. 
Now  as  B.  went  at  the  rate  of  10  miles  per  hour  for 
25  hours,  10x25=250  miles,  the  2d  Ans. 


(5)    Thus^=J)750 


187  50  whole  price  of  the  damaged. 
100        loss. 


87  50  what  it  sold  for. 


Then  $1  25cts,  :  g87  50c^^.  : :  1yd,  :  lOyds.zzzqmn- 

tity  damaged. 
And  70  X  4=2S0yds,  the  whole  quantity. 
70 

210  undamaged. 


And    ^750  OOd*.  cost. 

87  50  received  for  the  damaged. 

2l0yds,  :  $662  50  :  :   1  :  g3  I5lcts.+     Ans. 


160  PKOMISCUOUSf  EXAMPLES.. 

(6)    Thus  lOGO— 1=:=999  number  of  terras— 1.  ♦ 
1  ft.  common  dilTerence. 


999 
2  ft.,  first  term. 

1001  last  term. 
2 

1003  sum  of  the  terms. 
1000 

2)1003000 

3)501500  ft. 

220)167166+2  ft. 

0)759+186  yds. 

94+7/wy.  UQyds.  2ft.     Ans. 


(7)     Thus  admit  the  wall  to  contain  3600  feet. 

Then  20)3600(180  feet  raised  in  a  day  by  A.  B.  &  C. 
24)3600(150  *  B.  C.  &D. 

30)3600(120  C.  D.&  A. 

36)3600(100  A.  B.  &  D. 


3)550 
1 83i  feet  per  day  by  altogether. 


Then  183  J-  And  183.} 

B.  C..&  D.  150         C.  D.  &  A.  120 


A.     33} 


PROMISCUOUS  EXAMPLES. 


161 


And  183 


A.  B.  &D.  100 
C.  "83^ 


^  And  183  J 

A.  B.  &  C.  180' 


D. 


days. 


Then,  feet  per  day  by  A.  33J)3600(108  for  A.  to  do  it  in. 
do.  by  B.  63fj3600(56|J      B.         do. 

do.  by  C.  831)3600(43].        C.         do. 

do.  byD.    31)3600(1080     D.        do. 

And  1831)3600(19^    days    all   working  together. 
Ans. 


d,  d, 

(8)     Thus  4  crowns  at  146  each=584 


3  dolls. 
2  ducats 


108 
136 


1180c;.  sum. 


And  £1055  155.=253380cif. 


Then 
1180  :  253380 


d. 

584 
324 

272 


d,  d. 

125402-rl46=:858f|cr. 

69572 " 

58406 


2-rl46=:858f|cr.  ) 
2-T-108=644^5^g.  \ 
6-M36=429||<£wc.  ^ 


Ans. 


(9)     Thus  9wi.  :  21m.  :  :  g332  50c<5.  :  $775  83jc«5.  Ans. 
For  33250X21=698250  the  dividend. 
And  9=the  divisor. 
Then  698250^9=^775  ^^Ids. 

O  % 


162  PROMISCUOUS  EXAMPLES. 

(10)  Thus  12 

4 

16yrs.=10.n3'711  Table  IV. 
Time  of  reversion  12      =  8.86325       do. 


1.97462  difference. 
720.25  annuity. 


987260 
394904 
3949040 
1382164 

gl422. 1480300 

Or  ^1422  14cls,'  8m.+     Ans. 


(11)     3150  gigs  — 
2250 
X  Sets, 


igs~7X  5=^    g    cts, 
)  wagons  wh.  >  135  00  for  the  wagons. 
cts.=  3 

3150  gigs -f- 3  X  5=^ 
5250  footmen  wh.  >   52  50  for  footmen. 
X  let.—  ) 

6250  footmen  -r- 6  X  4  ^ 
=  3500  horsemen  >   70  00  for  horsemen, 
which  X  2ds*=       y 
3150  gjs  at  4cts.  per  )  j^g  ^^  ^^^  ^j^^ 


Amount  of, toll  383  60    Ans. 


(12)     Thus  15^a/5.  in  3min.~5gals.  per  min.  that  nm  in. 
And  20-7-5=  l/.:flf7*.  that  run  out  in  a  min.     Con- 
sequently, the  gain  is  5 — 4=^gaL  per  min.  which 
is  OOgnh.  per  hour. 
Then  nO-'60=50^<»vTA?.  yet  to  nm  in. 
Then  Sgals,  :  SOgals,  :  :   Imwi.  :   107nm.     Ans. 


PROMISCUOUS  EXAMPLES. 


163 


(13) 


Thus  264 
6 

6 
3 

1 

15  84  Int.  for  1  year. 

7  92 
3  96 

1 1  88  Int.  for  9  months. 
264  00 
30  00  profit. 

g305  88  for  the  whole. 

lbs  ^    cts  Wl 

Then  28cw?*.=3136)30588(0    9    7+     Ans. 
28224 


23640 
21952 


Rem.     1688 


(14)    Thus,  the  proportions  are  A.  4  B.  5  C.  3=12. 
Then  12  :  780 


'  4  :  260  A.'s  share  of  profit 

5  :  325  B.'s  do. 

'  3  :  195  C.'s  ,        do. 


1st 
Ans. 


pSO  proof. 

$    mo. 
Then  260x5=1300 
325X7=2275 
195X9=1755 

5330 


164                          PROMISCUOUS  EXAMPLES. 

r  1300  :   1405  36  A. 's  stock. 
Again  5330  ;  5762  : :    \  2275  :  2459  39  B.'s 
(  1755  :   1897  25  C's 

g5762  00  proof. 

Now  2459  39 

2087  00  B.  received. 

372  39  B.'s  loss  of  stock. 
And  325  00        do.     of  gain. 

Ans.  '^697  39  A.  &  C.  would  gain. 

(15)     1004-51=105  75.                          $  cts.m. 

Then  105  75  :  100  :  :  1000  :  945  62  6  cost  C. 

20  75  0  less. 

$924  87  6  cost  B. 

Again  100 

—5  50 

94  50  :  100  : :  g924  Slds,  6m,  :  g978  llOcts. 
4m.  that  the  whole  cost  A.  which  ~20AM^.=g48 
93c^*.  5m. -f  Tperhhd.     Ans. 

(16)             10X11=110  sold  for. 
10  X   7=  70  worth. 

$40  gain  of  A. 

$  ds,  m.                               $  ctt. 

And  110-r3=  36  66  6+  paid  cash.             5  25 

110  00  0                                  4  50 

$73  33  3  to  pay  in  paper.  $0  75  B.  gains. 

1            Then  450  :   75  :  :  73  33  3  :  $12  22ds.  2m.  gain  of 
1                 B.  $40— $12.22.2=r$^27.77.8.    Ans. 

PROMISCUOUS  EXAMPLES.  165 

(17)     Thus  21—14=7  years  to  be  of  age. 
Then  gl  300 
6 

'  7800  int.  first  year. 

1300 

1273  amount— 100. 

6 

7668  int.  second  year. 
1278 


125468  amount— 100. 
•6 


752808  intnhird  year. 
125468 


12299608  amount— 100. 
6 


73797648  int.  fourth  year. 
12299608 


12037584  amount— 100. 
6 


72225504  int.  fifth  year. 
12037584 


11759839  amount— 100. 
6 


70559034  int.  sixth  year. 
11759839 


11465429  amount— 100. 
6 


68792574  int.  seventh  year. 
11465429 


^ i  1 15.33.54m.  amount— 100.     Ans. 


IGG                          PROMISCUOUS  EXAMPLES. 

Another  solution : 

First,  1.067=1.5036302.     See  table  II.  Arithmetic. 

And    1.5036302X1300=1954.719.     Amount   at  .  Com- 
pound Interest. 

Also,  8.393837X100=839.383.     Amount  of  glOO  An- 
nuity for  7  years,  table  III. 

Hence  S5l954.719—g839.383==glll5  23cts.  5m.     Ans. 

(18) 

E                                  B                               F 

64 

^K 

^'^""— — ^ 

14 
D 

50 

C      76~^ 

L                                Statue,                           L 

Thus,  referring  to  the  above  figure. 

A  B  is  a  perpendicular  line  erected  on  the  centre  of  the 
statue's  base,  which  forms  the  side  A  C  of  the  right 
angle  A  C  D ;  and  the  other  two  sides,  A  D  86  and  C  D 
76  are  given  to  find  the  length  of  the  side  A  C. 

Now  76^=5776  &  862=7396 
—5776 

x/1620diff.  (40.2-L  =  AC 

PROMISCUOUS  EXAMPLES.  167 

Then  40.2-|-14  the  difference  between  the  columns 
=54.2  the  whole  length  of  A  B.  Then  54.22= 
2937.64  &  972= 

that  is  A  E=9409 

—2937.64 


V6471.36=(80.44-f  for  E  B. 

+  76  that  is  BF 


14=DF  156.44=EBF 

14  156.44 


56  62676 

14  62576 

93864 

196  78220 
15644 


24473.4736 
196 


2^/^24669.4736=157  ft.  Ans. 


Note. — ^This  solution  snpposes  the  statue  to  be  lower  than  the 
columns  :  admitting  it  to  be  higher,  the  operation  will,  of  course, 
be  different;  but  may  readily  be  performed  from  the  one  here 
given. 


(19)     Isec.  :  47*ec.  : :  1150/?.  :  54050/?.     Ans. 


(20)     15m.  7/5/^=83820/?. 

Then  1150/?.  :  8382t)/?.   ::   Iscc,  :   Im.  I2{^pec, 
Ans. 


168  PROMISCUOUS  EXAMPLES. 

(21)    First  suppose  J  of  8.2245  in.  to  be  gold. 

4.1 1225=^  4. 1 1225  in.  of  sil. 

10.36  5.85 


2467350 
1233675 
4112250 


2056125 
3289800 
2056125 


42.6029100oz.g.  24.0566 625o5r.  sil. 
24.0566625  


66.6595725 
63 


3.6595725  error  of  excess. 


Again  suppose  |  of  8.2245  in.  to  be  gold,  the  rest  silver. 


2.7415=^- 
10.36 


5.4830=silver. 
6.85 


164490 
82245 
274150 

28.401 940o2r. 
32.075550 

60.477490 
63. 


274150 
438640 
274150 

32.075550oar.  sil. 


2. 5225 1 0  error  of  defect. 

[Seefolloiping  page< 


PROMISCUOUS  1&XAMPX.ES. 


169 


in  o 

o  Tt 
o  «> 

00  1— 

GO   1.^ 

O  GO 

d  d 


to    LO 

vn 

^ 

l>  1— ' 

o 

^  5 

(^ 

lo  X 

UO 

c^* 

1?^  o 

CD 

r-  ^ 

<-> 

to  UO 

(M 

05  G^ 

CO 

O  G^ 

CO  in 

CO 

GO  ©< 

II 

fl 

lO 

.Q^T3 

(^ 

^    !=! 

t- 

o  o 

O 

O  O 

o  o 

o 

O  10 

LO    O 

LO  CO 

Oi 

LO   O 

LO  G^ 

G>^  GO 

C5   CO 

<?^ 

Gv)  O 

G^  00 

'^  GO 

O  CO 

rf 

CO  CO 

O  O 

Oi  CO 

r-4    lO 

LO 

lO  >o 

O  CO 

^  G-f 

^  G^ 

05   ""^ 

-rf 

s^^  t- 

LO    CO 

CO  CO 

O  t- 

G^  Oi 

GO 

<3^  'f 

O    UO 

O  ^ 

>0  Tf 

CO    ©^ 

GO  ■^ 

a>  CO 

GO  5< 

CO  CO 

O  05 

Oi  "^ 

LO  "<* 

Lf5    LO 

CO  CO 

r-i  r-* 

0) 

^ 

•M 

ns 

C 

KJ 

m 
< 

Cf^ 

o 

M 

r/: 

a> 

O) 

> 

o 

-73 

s-j 

(C 

C3 

o 

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a^ 

en 

o 

GO 

o 

Tj* 

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GO 

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o 

CO 
CO 


170  PROMISCUOUS  EXAMPLES. 

Another  solution : 
oz.      oz.         oz. 
First  63-^8.2245=7.66  weight  of  a  cubic  incli  of  the 

mixture. 
Til        "7  ftA  5  10.36s^r=1.81  proportional  hulk  of  gold, 
inen    7.t)t)  ^   5,85^=2.7  proportional  huJk  of  silver. 

Also  1.81X10.36±=18.7516  proportional  trei^^,«  of  gold. 
And  2.7  X   6.85=15.795    proportional  lOCTg*^  of  silver. 

34.5466  sum. 


oz. 

Hence  34.5466  :  18.7516  :  :  63  :  34.19587  gold       )  > 
And       34.5466  :  15.795     :  :  63  :  28.80356  silver.   ^  " 


Proof  62.99943 


(22)  Thus  llhs,  beef  at  5jcf5.=40}cfe. 

5     bread  at  6        =30 
Then  AO\cts,  :  g34  50cts. : :  30cf^. :  $25  lids.  4wi.+ 
Ans. 

(23)  Thus^oflof  JJf=^V 
Then  l^/^«^=fif||.     Ans, 


(24)  1000 

6 

60|00  int.  for  1  year. 
8 


int.  for  8  years. 


PROMISCUOUS  EXAMPLES.  171 

Then  8  years. 
6  per  cent. 

48 
100 

148  amt.  of  JJlOO  for  8  yrs.  at  5  per  cent 


$       $  $  $    c«*-"»- 

Then  148  :  100  : ;  1000  ;    675  67  5  the  present  worth. 
1000  00  0 


g324  32  5  discount. 
480  00  0  interest. 


Ans.  gi55  67  5  difference. 


(25)  V32=p5.656-|- 

v^24=4.9 


10.556  sum. 
V67  =4.06+ 


Ans.   6.496  difference. 


(26)     Thus   glOO   :   ^105|   :  :    $24.30    :    ^2587  20cf*. 
Ans. 


(27)    Thus  the  amount  of  gsOO  lods,  for  9  months  at  6 
per  cent.=::g533  2nds.  4m. 


172  PROMISCUOUS  EXAMPLES. 

cts,      ^    CU. 
And  5064x21=126  60  price  of  the  boards. 
140X13=  10  20     do.  tallow. 


144  80  amt. 
623  28  4 


§378  48  4  to  receive  in  flayseed. 

Then  as  ^Z\cts.:  §378  48c«#.  4m.  : :  Ihu,  :  409j|J6w. 
Ans. 


(28)  9  yrs.=36  qrs.  the  sum  of  terms. 

—1 

35 
3  common  difference. 

105 

-f  6=lst  term. 

Ill  last  term. 
6= let  term. 

117  sum. 
X  36  number  of  termi. 

702 
351 


2)4212 

g21.06cf*.  duehim.    Ans. 


PKOMISCUOUS  EXAMPLES.  173 

(29)     Thus  Syrs, — 2\yrs.:=^2lyrs, 

Then  1.06x1.06x1.045=1.174162  divisor. 
And    2363.3875  —  1.174162  =  ^2012    ^2cts,    ^m, 
Ans. 


(30)  Thus,  from  January  14th,  1802,  till  July  5th, 
1807,  inclusive=5  years  173  days.  And  the 
amount  of  jjl 854.69  for  that  time  at  5  per  cent 
per  annum  = 


^2362.3161 

285.  paid  off. 

2077.3161  second  bond. 
4| 


83092644 

10386580 

5193290 


98.67.2514  int.  of  the  2d  bond  for  1  yr. 


Then  98672514    :    365    :  :   52.65   :    194  days  the 
time  of  the  second  bond. 


Now  2077.3161 

52.65      interest. 


2129.9661  amount. 
102.43      paid  off. 


2027.5361  3d  bond. 


!>£> 


174  PROMISCUOUS  EXAMrLES. 

Which  was  out  from  J«nnary  12,  1808,  till  Octo- 
ber 26th,  1813,  whiuh  L^  5.789  years. 

$9Aj7.0M3  last  amount. 
20'27.5361  last  bond. 


469.4962  gained  on  the  last  bond, 

'' —      which  was  out  5.789. 

years,  and  this  bond 
inclusive  to  the  time 
=  11737.4064829. 

Then    11737.4064829   :  469.4962  ;  :  100  :   4  per 
cent.     Ans. 


(31)  First  suppose  10  horses  at  50=500 
20  cows  20=400 
60  sheep  4=240 


51110  sum. 
45 

684  error  of  excess. 


3    $ 

Agam  suppose  8  horses  at  50=400 
16  cows         20=320  ' 
48-  sheep  4=  1 92 


g912  sura. 
456 

456  error  of  excess. 


PROmSCUOUS  EXAMPLES.  175 

Then  684  x  8=:5472 
456X10=^4560 

Difference  of  errors=228)9 12(4  horses. 
912 


$      $ 
For  4  horses  at  50—200  ) 

Scows        20=160  >Ans. 
24  sheep         4=  96  ) 


55456  proof. 


Another  solution: 

$ 

First  50  price  of  each  horse. 
20x2=40  price  of  cows  for  each  horse. 
4x  6=24  price  of  sheep  for  each  hbrse 

114)456(4  numher  of  horses. . 
456 


$       $ 
Then   4  horses  at  50=200 

4X2=  Scows        20=160 

And  8x3=24  sheep         4=  96 


456  proof. 


176  PEOMISCUOUS  EXAMPLES. 

(32)         Thus  r  16--V    =  6 

Mean  rate  19  ?  17>,  )  =  5 


3+2=5 

oz,  oz, 

mi  r      in       ^5  :  10  of  17  carats  fine.  )  .^^ 

Then  as  5  :  10  : :  J  5  ^  ^0  ^^  24  carats  fine.  \  ^''^' 


(33)     £100  :  jei20  :  :  £230  5*.  :  £276  6*.  the  amount 
in  sterling. 
Then  as  £l  :  £276  65.  : :  J4  44c««.  4m.  :  gl227 
filets.  7wi.4-     Ans. 


(34)  Thus  f^'ff+J=l4|,  and  |||  subtracted  from  1= 

^|^=the  27  feet. 
Then  if|  :  nft.  : :  1  :  113/55.  4m.     Ans. 

(35)  $1  :  56jc?5.  :  :  $400  :  $32  14fd5.     AnS. 
(36) 


Thus    30 
+96 

126  sum. 
25  number  of  terms. 

630 
252 

2)3150 

$15.75 

Ans. 

BOMISCUOUS  EXAMPLES.  177| 

(37)    Thus  4  :  9  t :  47  :  105.75  the  greater  number. 
47 


152.75  sum. 
58.75  differ ence. 


76375 
106925 
122200 
76375 

Product    8974.0625    Ans. 


TBS  CND. 


v> 


^f^ 


'->/  ^^ 


